counterexamples on l_p maximal regularity we establish a transference result for l p maximal regularity for the abstract cauchy problem on banach space from this result we deduce counterexamples to l p maximal regularity 1 p infty in particular we obtain an operator b without any l p maximal regularity although it admits bounded imaginary powers with vert b is vert 1 for all s in mathbb r we also derive an operator which satisfies l p maximal regularity on bounded intervals 0 t but not on the half line mathbb r

forward propagation of time evolving acoustic pressure formulation and investigation of the impulse response in time wavenumber domain the aim of this work is to continuously provide the acoustic pressure field radiated from nonstationary sources from the acquisition in the nearfield of the sources of a planar acoustic field which fluctuates in time the method gives instantaneous sound field with respect to time by convolving wavenumber spectra with impulse response and then inverse fourier transforming into space for each time step the quality of reconstruction depends on the impulse response which is composed of investigated parameters as transition frequency and propagation distance sampling frequency also affects errors of the practically discrete impulse response used for calculation to avoid aliasing the impulse response is low pass filtered with chebyshev or kaiser bessel filter another approach to implement the impulse response consists of applying an inverse fourier transform to the theoretical transfer function for propagation to estimate the performance of each processing method a simulation test involving several sou

the h calculus and sums of closed operators we develop a very general operator valued functional calcu lus for operators with an h 1 calculus we then apply this to the joint functional calculus of two commuting sectorial operators when one has an h 1 calculus using this we prove theorem of dore venni type on sums of commuting sectorial operators and apply our results to the problem of lp maximal regularity our main assumption is the r boundedness of certain sets of operators and therefore methods from the geometry of ba nach spaces are essential here in the final section we exploit the special banach space structure of l1 spaces and c k spaces to obtain some more detailed results in this setting

on the inverse of the sum of two sectorial operators abstract we study an abstract linear operator equation on a banach space by using the inverse of the sum of two sectorial operators we prove that the boundedness of a special type of operator valued h calculus is sufficient for maximal regularity of the solution we apply the result to the abstract parabolic problem to give a maximal l p regularity condition we also study the abstract hyperbolic problem and give a sufficient condition for the existence of solution

numerical analysis of conservative and entropy schemes for the fokker planck landau equation conservatives and entropy schemes for the fokker planck landau fpl equation are studied we prove the existence of a unique positive and global in time solution for the homogeneous linear and nonlinear discretized either in the velocity space or both in the velocity space and in time fpl equation the stability analysis of these schemes leads to sufficient conditions on the time step that guarantee positivity and entropy decay

a nonlinear mixed finite eelement method for a degenerate parabolic equation arising in flow in porous media we study a model nonlinear degenerate advection diffusion equation having application in petroleum reservoir and groundwater aquifer simulation the main difficulty is that the true solution is typically lacking in regularity therefore we consider the problem from the point of view of optimal approximation through time integration we develop a mixed variational form that respects the known minimal regularity and then we develop and analyze two versions of a mixed finite element approximation a simpler semidiscrete time continuous version and a fully discrete version our error bounds are optimal in the sense that all but one of the bounding terms reduce to standard approximation error the exceptional term is a nonstandard approximation error term we also consider our new formulation for the nondegenerate problem showing the usual optimal l 2 error bounds moreover superconvergence is obtained under special circumstances

boundedness of riesz transforms for elliptic operators on abstract wiener spaces let e h be an abstract wiener space and let dv vd where d denotes the malliavin derivative and v is a closed and densely defined operator from h into another hilbert space h given a bounded operator b on h coercive on the range r v we consider the operators a v bv in h and a vv b in h as well as the realisations of the operators l dv bdv and l dvdv b in lp e and lp e h respectively where 1 p our main result asserts that the following four assertions are equivalent 1 d l d dv with lf p dvf p for f d l 2 l admits a bounded h functional calculus on r dv 3 d a d v with ah vh for h d a 4 a admits a bounded h functional calculus on r v moreover if these conditions are satisfied then d l d dv2 d da the equivalence 1 4 is a non symmetric generalisation of the classical meyer inequalities of malliavin calculus where h h v i b 12i a one sided version of 1 4 giving lp boundedness of the riesz transform dv l in terms of a square function estimate is also obtained as an application let a generate an analytic c0 contraction semigroup on a hilbert space h and let l be the lp realisation of the generator of its second quantisation our results imply that two sided bounds for the riesz transform of l are equivalent with the kato square root property for a the boundedness of the riesz transform is used to obtain an lp domain characterisation for the operator l

extension of measurement surface in near field acoustic holography in near field acoustic holography when measurements are made over a limited surface there has been recent interest in numerically enlarging the measurement surface tangentially current algorithms use iterative methods to extrapolate the field tangentially outward an algorithm based on the method of superposition is applied here which may be used to either extrapolate the field to enlarge the measurement surface or to interpolate in case there is a hole in the measurement surface where data are not available

a finite volume scheme for nonlinear degenerate parabolic equations we propose a second order finite volume scheme for nonlinear degenerate parabolic equations which admit an entropy functional for some of these models porous media equation drift diffusion system for semiconductors it has been proved that the transient solution converges to a steady state when time goes to infinity the present scheme preserves steady states and provides a satisfying long time behavior moreover it remains valid and second order accurate in space even in the degenerate case after describing the numerical scheme we present several numerical results which confirm the high order accuracy in various regime degenerate and nondegenerate cases and underline the efficiency to preserve the large time asymptotic

product formulas in functional calculi for sectorial operators we study the product formula fg a f a g a in the framework of unbounded functional calculus of sectorial operators a we give an abstract result and as corollaries we obtain new product formulas for the holomorphic functional calculus an extended stieltjes functional calculus and an extended hille phillips functional calculus our results generalise previous work of hirsch martinez and sanz and schilling

numerical algorithms for axisymmetric fokker planck landau operators we establish a simplified form of the axisymmetric fokker planck landau operator in doing so we derive a weak formulation of this operator on which we get directly the conservation properties and the decay of the entropy as it is the case for the three dimensional operator a symmetrized version of this formulation leads to a class of numerical schemes which satisfy these physical properties at the discrete level fast numerical algorithms used in previous works are shown to be efficient in the cylindrical geometry finally some numerical tests are presented at the end of this paper

subordinated discrete semigroups of operators given a power bounded linear operator t in a banach space and a probability f on the non negative integers one can form a subordinated operator s k 0 f k t k we obtain asymptotic properties of the subordinated discrete semigroup s n n 1 2 under certain conditions on f in particular we study probabilities f with the property that s satisfies the ritt resolvent condition whenever t is power bounded examples and counterexamples of this property are discussed the hypothesis of power boundedness of t can sometimes be replaced by the weaker kreiss resolvent condition

martingale transforms and complex uniform convexity les transformees de martingale et les operateurs integraux singuliers de calderon zygmund sont bornees comme des operateurs de l 2 l 1 dans l 2 l q quand 0 q 1 si y est un sous espace reflexif de l 1 alors l 1 y peut se renormer pour etre 2 complexe uniformement convexe on donne une nouvelle demonstration de la propriete de cotype 2 de l 1 h

discrete velocity models and numerical schemes for the boltzmann bgk equation in plane and axisymmetric geometries we present new numerical models for computing transitional or rarefied gas flows as described by the boltzmann bgk and bgk es equations we first propose a new discrete velocity model based on the entropy minimization principle this model satisfies the conservation laws and the entropy dissipation moreover the problem of conservation and entropy for axisymmetric flows is investigated we find algebraic relations that must be satisfied by the discretization of the velocity derivative appearing in the transport operator then we propose some models that satisfy these constraints owing to these properties we obtain numerical schemes that are economic in terms of discretization and robust in particular we develop a linearized implicit scheme for computing stationary solutions of the discrete velocity bgk and bgk es models this scheme is the basis of a code which can compute high altitude hypersonic flows in 2d plane and axisymmetric geometries our results are analyzed and compared to other methods

conservative finite difference schemes for the fokker planck equations not violating the law of an increasing entropy abstract two finite difference schemes for the fokker planck equation in the case of an isotropic function of the charge particles are constructed these schemes are first order accurate with respect to time and second order accurate with respect to a e 2 the schemes conserve the number of particles and energy and the entropy change is nonnegative a relation between the incresing entropy law and the stability of the finite difference schemes is established

the spectral collocation method for the kinetic equation with the nonlinear two dimensional coulomb collisional operator the spectral collocation method is used for numerical solution of the fokker planck equation with nonlinear integro differential coulomb collisional operator the spectral collocation method in general gives superior results to the usually employed finite difference method approximation high order approximation of the integro differential operator by the spectral collocation is able to provide highly accurate results on sparse grids approximation of the boundary conditions of the problem is very straightforward and natural the method is also capable of easily accounting for the physically important conservation properties of the system in this article the details of the numerical implementation of the fokker planck equation solver with coulomb collisional operator are discussed some test results are presented and certain limitations of the implementation are discussed the method is applied to the problem of plasma heating by superthermal radiation the self similar solution is obtained for this case

some results about complex powers of closed operators the aim of this paper is to give some further results about complex powers of operators a tool that the authors already employed in 2 and s to study some questions of operator theory our first result is essentially a completion of corollary 2 9 of 2 since it gives an estimate for the rate of decrease of a a at infinity when a is a positive operator with bounded imaginary powers we remark that the converse question i e the estimate of the imaginary powers in terms of the amplitude of the spectrum remains open next we prove a result of pertubation if we add to a positive operator

finite element approximation of the transport of reactive solutes in porous media part 1 error estimates for nonequilibrium adsorption processes in this paper we analyze a fully practical piecewise linear finite element approximation involving numerical integration backward euler time discretization and possibly regularization of the following degenerate parabolic system arising in a model of reactive solute transport in porous media find u x t v x t such that begin eqnarray partial t u partial t v delta u f quad mbox in omega times 0 t qquad u 0 quad mbox on partial omega times 0 t partial tv k varphi u v quad mbox in omega times 0 t u cdot 0 g 1 cdot quad v cdot 0 g 2 cdot quad mbox in omega subset real d quad 1 le d le 3 end eqnarray for given data k in real f g 1 g 2 and a monotonically increasing varphi in c 0 real cap c 1 infty 0 cup 0 infty satisfying varphi 0 0 which is only locally holder continuous with exponent p in 0 1 at the origin e g varphi s equiv s p this lack of lipschitz continuity at the origin limits the regularity of the unique solution u v and leads to difficulties in the finite element error analysis

viscous splitting approximation of mixed hyperbolic parabolic convection diffusion equations we first analyse a semi discrete operator splitting method for nonlinear possibly strongly degenerate convection diffusion equations due to strong degeneracy solutions can be discontinuous and are in general not uniquely determined by their data hence weak solutions satisfying an entropy condition are sought we then propose and analyse a fully discrete splitting method which employs a front tracking scheme for the convection step and a finite difference scheme for the diffusion step numerical examples are presented which demonstrate that our method can be used to compute physically correct solutions to mixed hyperbolic parabolic convection diffusion equations

spectral methods for the non cut off boltzmann equation and numerical grazing collision limit in this paper we study the numerical passage from the spatially homogeneous boltzmann equation without cut off to the fokker planck landau equation in the so called grazing collision limit to this aim we derive a fourier spectral method for the non cut off boltzmann equation in the spirit of 21 23 we show that the kernel modes that define the spectral method have the correct grazing collision limit providing a consistent spectral method for the limiting fokker planck landau equation in particular for small values of the scattering angle we derive an approximate formula for the kernel modes of the non cut off boltzmann equation which similarly to the fokker planck landau case can be computed with a fast algorithm the uniform spectral accuracy of the method with respect to the grazing collision parameter is also proved

solution of degenerate convection diffusion problems by the method of characteristics a new approximation scheme is proposed to solve nonlinear degenerate convection diffusion problems the method is based on a relaxation scheme developed for degenerate parabolic problems in w jager and j kacur numer math 60 1991 pp 407 427 m2an math model numer anal 29 1995 pp 605 627 and on the method of characteristics j douglas and t i russell siam j numer anal 19 1982 pp 871 885 o pironneau numer math 38 1982 pp 309 332

the gauss green theorem and removable sets for pdes in divergence form abstract applying a very general gauss green theorem established for the generalized riemann integral we obtain simple proofs of new results about removable sets of singularities for the laplace and minimal surface equations we treat simultaneously singularities with respect to differentiability and continuity

a finite volume scheme for the patlak keller segel chemotaxis model a finite volume method is presented to discretize the patlak keller segel pks modeling chemosensitive movements first we prove existence and uniqueness of a numerical solution to the proposed scheme then we give a priori estimates and establish a threshold on the initial mass for which we show that the numerical approximation converges to the solution to the pks system when the initial mass is lower than this threshold numerical simulations are performed to verify accuracy and the properties of the scheme finally in the last section we investigate blow up of the solution for large mass

the conception of structure borne sound based near field holography abstract a procedure for the projection of structure borne sound fields is introduced following the basic idea behind near field acoustic holography it is shown that the bending wave field of an infinite plate subjected to point force excitation can be reconstructed by means of fourier transform based wave field extrapolation all required information on the wave field is obtained by vibrational response measurement in the near field of the excitation using a circular geometry with a limited number of positions the procedure is verified both numerically and experimentally to very satisfying results the experiments indicate that the reconstruction at the source becomes erratic when standoff distances greater than half of the minimum wavelength under consideration are used reconstruction of the far field plate response is found to be less restrictive

the measurement of plane wave reflection coefficients by using two dimensional spatial transforms recently tamura has proposed a method for measuring plane wave reflection coefficients at arbitrary angles of incidence m tamura proceedings of inter noise 89 1085 1088 1989 the procedure is based on measuring the complex pressure distribution on two parallel planes located between a compact source and the reflecting surface by spatially transforming the measured data into the wave number domain the sound field may be decomposed into upward and downward going plane wave components the reflection coefficient is then simply the ratio of the complex amplitudes of the upward and downward going plane wave components at a particular angle of incidence in this presentation the fundamentals of the technique will be reviewed followed by the presentation of new results that illustrate the effect of source type and location on measurement accuracy and practicality in addition it will be shown that acceptable accuracy may be achieved using reasonable spatial aperture sizes and sample rates only if the spatial data are transformed using a hankel transform based on a cylindrical geometry rather than a two dimensional fourier transform based on a rectangular geometry finally it will be shown that the use of a generalized hankel transform can eliminate the usual requirement that the source radiate a cylindrically symmetric sound field both simulated and model scale experiments will be used to show that the technique yields accurate results when the source type and transform geometry are chosen appropriately

identification of asymptotic decay to self similarity for one dimensional filtration equations the objective of this paper is the derivation and the analysis of a simple explicit numerical scheme for general one dimensional filtration equations it is based on an alternative formulation of the problem using the pseudoinverse of the density s repartition function in particular the numerical approximations can be proven to satisfy a contraction property for a wasserstein metric various numerical results illustrate the ability of this numerical process to capture the time asymptotic decay towards self similar solutions even for fast diffusion equations

reconstruction of vibroacoustic fields in half space by using hybrid near field acoustical holography in this paper we examine the accuracy and efficiency of reconstructing the vibroacoustic quantities generated by a vibrating structure in half space by using hybrid near field acoustic holography nah and modified helmholtz equation least squares hels formulations in hybrid nah we combine modified hels with an inverse boundary element method ibem to reconstruct a vibroacoustic field the main advantage of this approach is that the majority of the input data can be regenerated but not measured thus the efficiency is greatly enhanced in modified hels we expand the field acoustic pressure in terms of outgoing and incoming spherical waves and specify the corresponding expansion coefficients by solving a system of equations obtained by matching the assumed form solution to the measured acoustic pressure here the system of equations is ill conditioned and tikhonov regularization is implemented through singular value decomposition svd and the generalized cross validation gcv method numerical examples of a dilating and oscillating spheres and finite cylinder are demonstrated test results show that hybrid nah can yield a more accurate reconstruction than does a modified hels but a modified hels is more efficient than is hybrid nah work supported by nsf

a numerical method for the accurate solution of the fokker planck landau equation in the nonhomogeneous case abstract a new approach for the accurate numerical solution of the fokker planck landau fpl equation in the nonhomogeneous case is presented the method couples through a time splitting algorithm a finite volume scheme for the transport with a fast spectral solver for the efficient solution of the collision operator recently introduced the scheme allows the use of different grids in the velocity space for the transport and the collision phases the use of a suitable explicit runge kutta solver for the time integration of the collision phase permits avoid once of excessive small time steps induced by the stiffness of the diffusive collision operator numerical results for both space homogeneous and space nonhomogeneous situations show the efficiency and the accuracy of the present method

implicit schemes for the fokker planck landau equation we propose time implicit schemes to solve the homogeneous fokker planck landau equation in both the isotropic and 3 dimensional geometries these schemes have properties of conservation and entropy moreover they allow for large time steps making them faster than the usual explicit schemes to solve the involved linear systems we prove that the use of krylov like solvers preserves the conservation properties we show in particular that the conjugate gradient method can be used numerical tests are performed for the isotropic case and demonstrate an important gain in terms of cpu time with the same accuracy as explicit schemes this work is a first step to the development of fast implicit schemes to solve a class of inhomogeneous kinetic equations

high order relaxation schemes for nonlinear degenerate diffusion problems several relaxation approximations to partial differential equations have been recently proposed examples include conservation laws hamilton jacobi equations convection diffusion problems and gas dynamics problems the present paper focuses on diffusive relaxation schemes for the numerical approximation of nonlinear parabolic equations these schemes are based on a suitable semilinear hyperbolic system with relaxation terms high order methods are obtained by coupling eno and weighted essentially nonoscillatory weno schemes for space discretization with implicit explicit imex schemes for time integration error estimates and a convergence analysis are developed for semidiscrete schemes with a numerical analysis for fully discrete relaxed schemes various numerical results in one and two dimensions illustrate the high accuracy and good properties of the proposed numerical schemes also in the degenerate case these schemes can be easily implemented on parallel computers and applied to more general systems of nonlinear parabolic equations in two and three dimensional cases

a combined finite volume nonconforming mixed hybrid finite element scheme for degenerate parabolic problems we propose and analyze a numerical scheme for nonlinear degenerate parabolic convection diffusion reaction equations in two or three space dimensions we discretize the diffusion term which generally involves an inhomogeneous and anisotropic diffusion tensor over an unstructured simplicial mesh of the space domain by means of the piecewise linear nonconforming crouzeix raviart finite element method or using the stiffness matrix of the hybridization of the lowest order raviart thomas mixed finite element method the other terms are discretized by means of a cell centered finite volume scheme on a dual mesh where the dual volumes are constructed around the sides of the original mesh checking the local peclet number we set up the exact necessary amount of upstream weighting to avoid spurious oscillations in the convection dominated case this technique also ensures the validity of the discrete maximum principle under some conditions on the mesh and the diffusion tensor we prove the convergence of the scheme only supposing the shape regularity condition for the original mesh we use a priori estimates and the kolmogorov relative compactness theorem for this purpose the proposed scheme is robust only 5 point 7 point in space dimension three locally conservative efficient and stable which is confirmed by numerical experiments

long time asymptotics of a multiscale model for polymeric fluid flows in this paper we investigate the long time behavior of some micro macro models for polymeric fluids hookean model and fene model in various settings shear flow general bounded domain with homogeneous dirichlet boundary conditions on the velocity general bounded domain with non homogeneous dirichlet boundary conditions on the velocity we use both probabilistic approaches coupling methods and analytic approaches entropy methods

a finite volume scheme for convection diffusion equations with nonlinear diffusion derived from the scharfetter gummel scheme we propose a finite volume scheme for convection diffusion equations with nonlinear diffusion such equations arise in numerous physical contexts we will particularly focus on the drift diffusion system for semiconductors and the porous media equation in these two cases it is shown that the transient solution converges to a steady state solution as t tends to infinity the introduced scheme is an extension of the scharfetter gummel scheme for nonlinear diffusion it remains valid in the degenerate case and preserves steady states we prove the convergence of the scheme in the nondegenerate case finally we present some numerical simulations applied to the two physical models introduced and we underline the efficiency of the scheme to preserve long time behavior of the solutions

on subordinated holomorphic semigroups if e is a uniformly bounded c0 semigroup on a complex banach space x then a 0 a 1 generates a holomorphic semigroup on x and e is subordinated to e through the levy stable density function this was proved by yosida in 1960 by suitably deforming the contour in an inverse laplace transform representation using other methods we exhibit a large class of probability measures such that the subordinated semigroups are always holomorphic and obtain a necessary condition on the measure s laplace transform for that to be the case we then construct probability measures that do not have this property

error analysis for characteristics based methods for degenerate parabolic problems we consider characteristics based finite element methods for solving nonlinear degenerate advection diffusion equations these equations have applications in the simulation of petroleum reservoirs and groundwater aquifers and in the modeling of free boundary problems standard finite element galerkin methods have been studied for these equations in this paper we analyze the characteristics based finite element methods for them the main difficulty in the analysis is that the equations are degenerate and the solution lacks regularity here we develop a technique that respects the degeneracy and the known minimal regularity this technique is based on the green operator for standard elliptic equations and is developed directly for the degenerate advection diffusion equations we concentrate our analysis on the modified method of characteristics mmoc and one of its variants the modified method of characteristics with adjusted advection mmocaa which conserves mass we derive error estimates in various norms the extension to other variants is discussed the present technique is also applied to nondegenerate problems error estimates previously obtained for the mmoc are derived under much weaker regularity assumptions on the solution and the error estimates for the mmocaa appear new even in the nondegenerate case finally numerical results are presented to show the sharpness of the error estimates derived

separation of nonstationary sound fields in the time wavenumber domain a number of sound field separation techniques have been proposed for different purposes however these techniques just consider the separation of sound fields in the space domain and are restricted to stationary sound fields when the sound fields are nonstationary it is also necessary to perform the separation in the time domain therefore on the basis of the propagation principle of sound pressure in the time wavenumber domain a nonstationary sound field separation technique with two closely spaced parallel measurement surfaces is proposed it can separate the nonstationary signals generated by the primary sources in both time and space domains when the disturbing sources exist on the other side of the measurement plane the signals in time and space domains are separated by using the spatial fourier transform method and the time domain deconvolution method a simulation involving two monopoles driven by nonstationary signals demonstrates that the method proposed can remove the influence of disturbing sources in both time and space domains the feasibility of this method is also demonstrated by an experiment with two loudspeakers located on two sides of measurement planes additionally to comment more objectively on the separation results some indicators are computed in both the simulation and experiment

solution of porous medium type systems by linear approximation schemes the convergence of semi discrete and discrete linear approximation schemes is analysed for nonlinear degenerate parabolic systems of porous medium type the enthalpy formulation and variational technique are used the semi discretization used reduces the original parabolic p d e to linear elliptic p d e the algebraic correction arising from nonlinearities is treated by newton like iterations in finite steps some numerical experiments are discussed and compared with the analytical solutions

sound source identification in a noisy environment based on inverse patch transfer functions with evanescent green s functions abstract a modified inverse patch transfer function iptf method is used to reconstruct the normal velocities of the target source in a noisy environment the iptf method simplifies the helmholtz integral equation to one term by constructing a green s function satisfying neumann boundary conditions for an enclosure which is generally constructed by slowly convergent modal expansions the main objective of the present work is to provide an evanescent green s function to improve the convergence of calculations a brief description of the iptf method and two sets of green s functions for a rectangular cavity are presented firstly in simulations both the green s functions are used to calculate the condition numbers of impedance matrices describing the relation between source and measurement patches and the time cost of calculation based on the two sets of green s functions at 450 hz is compared double pressure measurements are then employed as the input data instead of pressure and velocity measurements the normal velocities of two baffled loudspeakers are reconstructed by the combination of a measurement method and a green s function in the presence of a disturbing source in the frequency range of 50 1000 hz in addition the double pressure measurements are examined by an experiment the precise identification of the sources indicates that the double pressure measurements are capable of localizing sources in a noisy environment it is also found that the reconstruction with the evanescent green s functions is slightly better than that with the modal expansions

resolvent representations for functions of sectorial operators abstract we obtain integral representations for the resolvent of a where is a holomorphic function mapping the right half plane and the right half axis into themselves and a is a sectorial operator on a banach space as a corollary for a wide class of functions we show that the operator a generates a sectorially bounded holomorphic c 0 semigroup on a banach space whenever a does and the sectorial angle of a is preserved when is a bernstein function this was recently proved by gomilko and tomilov but the proof here is more direct moreover we prove that such a permanence property for a can be described at least on hilbert spaces in terms of the existence of a bounded h calculus for a as byproducts of our approach we also obtain new results on functions mapping generators of bounded semigroups into generators of holomorphic semigroups and on subordination for ritt operators

the ritt property of subordinated operators in the group case abstract let g be a locally compact abelian group let be a regular probability measure on g let x be a banach space let g b x be a bounded strongly continuous representation consider the average or subordinated operator s g t d t x x we show that if x is a umd banach lattice and has bounded angular ratio then s is a ritt operator with a bounded h functional calculus next we show that if is the square of a symmetric probability measure and x is k convex then s is a ritt operator we further show that this assertion is false on any non k convex space x

an entropy scheme for the fokker planck collision operator of plasma kinetic theory we propose a finite difference scheme to approximate the fokker planck collision operator in 3 velocity dimensions the principal feature of this scheme is to provide a decay of the numerical entropy as a consequence it preserves the collisional invariants and its stationary solutions are the discrete maxwellians we consider both the whole velocity space problem and the bounded velocity problem in the latter case we provide artificial boundary conditions which preserve the decay of the entropy

nearfield acoustic holography nah ii holographic reconstruction algorithms and computer implementation the basic theory treating steady state acoustic radiation problems in the nearfield has been presented in several articles on nearfield acoustic holography in this article the approximations and assumptions necessary to reduce the infinite and continuous convolution integrals encountered in these problems to a finite and discrete form suitable for high speed numerical processing are illuminated theoretically and tested numerically to evaluate the convolution integrals two assumptions are made first the boundary field may be replaced with a patchwise constant field for reasonably small patches and second the field is negligible outside of a finite region with these two assumptions the problem reduces to one of representing the green s functions six methods of sampling or representing the green s functions are developed and these are compared theoretically and numerically

on the fokker planck boltzmann equation we consider the boltzmann equation perturbed by fokker planck type operator to overcome the lack of strong a priori estimates and to define a meaningful collision operator we introduce a notion of renormalized solution which enables us to establish stability results for sequences of solutions and global existence for the cauchy problem with large data the proof of stability and existence combines renormalization with an analysis of a defect measure

numerical approximation of the vlasov poisson fokker planck system in two dimensions a numerical method is developed for approximating the solution to the vlasov poisson fokker planck system in two spatial dimensions the method generalizes the approximation for the system in one dimension given in s wollman e ozizmir numerical approximation of the vlasov poisson fokker planck system in one dimension j comput phys 202 2005 602 644 the numerical procedure is based on a change of variables that puts the convection diffusion equation into a form so that finite difference methods for parabolic type partial differential equations can be applied the computational cycle combines a type of deterministic particle method with a periodic interpolation of the solution along particle trajectories onto a fixed grid computational work is done to demonstrate the accuracy and effectiveness of the approximation method parts of the numerical procedure are adapted to run on a parallel computer

examples of unbounded imaginary powers of operators two examples are given the first one consists of an operator of positive type in hilbert space without bounded imaginary powers the second one is concerned with the closedness of the sum of two closed operators in a hilbert space

a joint functional calculus for sectorial operators with commuting resolvents 1 introduction in this paper we are concerned with h 1 functional calculus in the sense of the construction introduced by mcintosh 23 and developed recently by cowling doust mcintosh and yagi 8 given v in 0 p we will use the notation sv fz 2 c n f0g jarg z j vg to denote the open sector of angle 2v around the half line r let x be a complex banach space given a linear operator a on x we denote by d a n a and r a the domain the kernel and the range of a respectively we also denote by j a the spectrum of a and by r a the resolvent set of a

numerical errors associated with the method of superposition for computing acoustic fields the method of wave superposition is based on the idea that an acoustic radiator can be approximately represented by the sum of the fields due to a finite number of interior point sources the accuracy of this representation depends upon how well the velocity boundary condition on the surface of the body is approximated the ultimate objective of this study then is to provide some guidelines for improving the accuracy of the surface velocity reconstruction and consequently the accuracy of the superposition solutions in general this is dependent upon the particular surface velocity distribution to be reconstructed as well as other formulation factors such as the acoustic wave number the number and locations of the surface nodes and the number and locations of the point sources velocity interpolation functions are introduced as a means of quantifying the dependence of reconstruction errors on the acoustic wave number and the placement of the surface nodes and point sources numerical experiments

maximum principle satisfying third order discontinuous galerkin schemes for fokker planck equations we design and analyze up to third order accurate discontinuous galerkin dg methods satisfying a strict maximum principle for fokker planck equations a procedure is established to identify an effective test set in each computational cell to ensure the desired bounds of numerical averages during time evolution this is achievable by taking advantage of the two parameters in the numerical flux and a novel decomposition of weighted cell averages based on this result a scaling limiter for the dg method with first order euler forward time discretization is proposed to solve the one dimensional fokker planck equations strong stability preserving high order time discretizations will keep the maximum principle it is straightforward to extend the method to two and higher dimensions on rectangular meshes we also show that a modified limiter can preserve the strict maximum principle for dg schemes solving fokker planck equations as a consequence the present schemes preserve steady states numerical tests

finite volume methods for convection diffusion problems derivation stability and error analysis in both discrete h 1 and l 2 norms for cell centered finite volume approximations of convection diffusion problems are presented various upwind strategies are investigated the theoretical results are illustrated by numerical examples

the completely conservative difference schemes for the nonlinear landau fokker planck equation conservativity and complete conservativity of finite difference schemes are considered in connection with the nonlinear kinetic landau fokker planck equation the characteristic feature of this equation is the presence of several conservation laws finite difference schemes preserving density and energy are constructed for the equation in one and two dimensional velocity spaces some general methods of constructing such schemes are formulated the constructed difference schemes allow us to carry out the numerical solution of the relaxation problem in a large time interval without error accumulation an illustrative example is given

erratum to perturbation and interpolation theorems for the h calculus with applications to differential operators we prove comparison theorems for the h calculus that allow to transfer the property of having a bounded h calculus from one sectorial operator to another the basic technical ingredient are suitable square function estimates these comparison results provide a new approach to perturbation theorems for the h calculus in a variety of situations suitable for applications our square function estimates also give rise to a new interpolation method the rademacher interpolation we show that a bounded h calculus is characterized by interpolation of the domains of fractional powers with respect to rademacher interpolation this leads to comparison and perturbation results for operators defined in interpolation scales such as the l p scale we apply the results to give new proofs on the h calculus for elliptic differential operators including schrodinger operators and perturbed boundary conditions as new results we prove that elliptic boundary value problems with bounded uniformly coefficients have a bounded h calculus in certain sobolev spaces and that the stokes operator on bounded domains with c 1 1 has a bounded h calculus in the helmholtz scale l p p 1

an equivalent source technique for calculating the sound field inside an enclosure containing scattering objects the equivalent source method has previously been used to calculate the exterior sound field radiated or scattered from bodies in the free field in this paper the method is used to calculate the internal pressure field for an enclosure which can have arbitrary boundary conditions and may include internal objects which scatter the sound some of the equivalent source positions are chosen to be the same as the first order images of the source inside the enclosure some are positioned within the scattering objects and the remainder are positioned on a spherical surface some distance outside the enclosure the normal velocity on the surfaces of the scattering objects and the enclosure walls is evaluated at a larger number of positions than there are equivalent sources the sum of the squared difference between this velocity and that expected because of the admittance of the boundary is minimized by adjusting the strengths of the equivalent sources the convergence of the method is checked by evaluating the velocity at a larger number of monitoring positions example results are presented for the sound field and frequency response inside a damped rectangular enclosure which compare very well with the conventional modal model the effect of having rigid spheres inside the enclosure are then investigated and it is found that the effect is significant even some distance from the spheres and at frequencies for which the size of the sphere is small compared to a wavelength finally the effect of a nonlocally reacting boundary condition is illustrated by assuming that one of the walls of the enclosure is an elastic plate

spatial fourier transform method of measuring reflection coefficients at oblique incidence i theory and numerical examples a new method using spatial fourier transform has been developed to measure reflection coefficients at oblique incidence the method involves the measurement of complex pressure distributions on two parallel planes lying close to the surface of a test material and decomposing each of the complex pressure distributions into plane wave components by using two dimensional spatial fourier transform the incident and reflected plane wave components on the surface of the test material can be mathematically separated by the use of plane wave propagation theory this separation leads to the determination of reflection coefficients at arbitrary angles of incidence investigation has been made into the error due to the finite size of the measurement area to show that the magnitude of the error can be reduced by using a dipole source instead of a monopole source numerical examples are given to illustrate the validity of the method

numerical approximation of the spatially homogeneous fokkerplancklandau equation a numerical method is developed for the spatially homogeneous fokkerplancklandau fpl equation for the case of coulomb collisions the equation is put into a form so that finite difference methods for parabolic type pdes can be applied through a transformation of variables the velocity space computation is reduced to a bounded domain and finite differencing is done with a well defined exact boundary condition corresponding to v at infinity for the discretization in time implicit differencing is used an analysis is carried out on the discrete approximation as applied to a linear fpl equation and for the linear equation it is proved that the numerical method is unconditionally stable and convergent computational work is then done that demonstrates the unconditional stability and accuracy of the numerical method for the nonlinear fpl equation

a sufficient condition for the carasso kato theorem so that f y 1 p dy cxz in 0 2 then remark 2 of 1 p 298 implies that a 0 p t x 0 for t 0 x 0 therefore for c 0 the inverse laplace transform for 0 1 leads to 2 1 theorem 7 6a of 2 p 69 in addition we add the following correction a lines 5 1 from bottom on p 335 will be changed as follows it is called the subordinated semigroup define the operator x a by

entropy decay of discretized fokker planck equations i temporal semidiscretization abstract in this paper we study the large time behavior of a fully implicit semidiscretization in time of parabolic fokker planck type equations using logarithmic sobolev inequalities exponential decay of the relative entropy w r t the steady state is proved which yields convergence of the discrete scheme towards the unique steady state the exponential decay rate recovers as at j 0 the decay rate of the original fokker planck type equations

sound field separation technique based on equivalent source method and its application in nearfield acoustic holography a technique for separating sound fields using two closely spaced parallel measurement surfaces and based on equivalent source method is proposed the method can separate wave components crossing two measurement surfaces in opposite directions which makes nearfield acoustic holography nah applications in a field where there exist sources on the two sides of the hologram surface in a reverberant field or in a scattered field possible the method is flexible in applications simple in computation and very easy to implement the measurement surfaces can be arbitrarily shaped and they are not restricted to be regular as in the traditional field separation technique and because the method performs field separation calculations directly in the spatial domain not in the wave number domain it avoids the errors and limitations the window effects etc associated with the traditional field separation technique based on the spatial fourier transform method in the paper a theoretical description is first

explicit diffusive kinetic schemes for nonlinear degenerate parabolic systems we design numerical schemes for nonlinear degenerate parabolic systems with possibly dominant convection these schemes are based on discrete bgk models where both characteristic velocities and the source term depend singularly on the relaxation parameter general stability conditions are derived and convergence is proved to the entropy solutions for scalar equations

a method for computing acoustic fields based on the principle of wave superposition a method for computing the acoustic fields of arbitrarily shaped radiators is described that uses the principle of wave superposition the superposition integral which is shown to be equivalent to the helmholtz integral is based on the idea that the combined fields of an array of sources interior to a radiator can be made to reproduce a velocity prescribed on the surface of the radiator the strengths of the sources that produce this condition can in turn be used to compute the corresponding surface pressures the results of several numerical experiments are presented that demonstrate the simplicity of the method also the advantages that the superposition method has over the more commonly used boundary element methods are discussed these include simplicity of generating the matrix elements used in the numerical formulation and improved accuracy and speed the latter two being due to the avoidance of uniqueness and singularity problems inherent in the boundary element formulation

a mapping relationship based near field acoustic holography with spherical fundamental solutions for helmholtz equation abstract in the procedure of the near field acoustic holography nah based on the fundamental solutions for helmholtz equation fs the number of fs and the measurement setup to obtain their coefficients are two crucial issues to the successful reconstruction the current work is motivated to develop a framework for the nah which supplies a guideline to the determination of the number of fs as well as an optimized measurement setup a mapping relationship between modes on surfaces of boundary and hologram is analytically derived by adopting the modes as fs in spherical coordinates thus reconstruction is converted to obtain the coefficients of participant modes on holograms in addition an integral identity is firstly to be derived for the modes on convex surfaces which is useful in determining the inefficient or evanescent modes for acoustic radiation in free space to determine the number of fs adopted in the mapping relationship based nah mrs based nah two approaches are proposed to supply reasonable estimations with criteria of point wise pressure and energy respectively a technique to approximate a specific degree of mode on patches by a set of locally orthogonal patterns is explored for three widely used holograms such as planar cylindrical and spherical holograms which results in an automatic determinations of the number and position of experimental setup for a given tolerance numerical examples are set up to validate the theory and techniques in the mrs based nah reconstructions of a cubic model demonstrate the potential of the proposed method for regular models even with corners and shapers worse results for the elongated cylinder with two spherical caps reveal the deficiency of the mrs based nah for irregular models which is largely due to the adopted modes are fs in spherical coordinates the nah framework pursued in the current work provides a new insight to the reconstruction procedure based on the fs in spherical coordinates

square function estimates and the kato problem for second order parabolic operators in rn 1 in 4 the kato square root problem for second order complex uniformly elliptic operators of the form l div a del f with only bounded and measurable coefficients was solved the solution is a

on the closedness of the sum of two closed operators o t t 1 where e g a is the infinitesimal generator of an analytic semigroup in a complex banach space x we find that in general it is false that for every fe lp 0 t x problem 1 has a solution uewi p o t x c lp o t a usually it is necessary to impose some further regularity conditions on f consider for instance the way in which problem 1 is studied in the paper 8 and compare th 3 7 and 3 14 which are applied in w 4 of the same paper to solve problem 1 we find that in general we have only strong solutions while in the hilbert space setting we have strict solutions this corresponds to the fact that in general the operator a b where b u u is only closable while in a hilbert space it is closed this remark suggests that the better result may depend on the nicer geometric properties of a hilbert space with respect to a general banach space and it is natural to ask which conditions should be imposed on the banach space to force the sum of two suitable closed opera tors to be closed the above considerations motivate the manifold aim of the present paper a to find conditions on a banach space x and on closed linear operators a and b acting in x which ensure that a b is closed b to apply the result of a to problem 1 it seems that the convenient property for the banach space x is convexity or otherwise stated the umd condition for information about these equiva lent conditions we refer to 4 in which it is also proved that if x is convex and l p oe then the hilbert transform is continuous from lp r x into lp r x on the other hand it is also known see 2 that if there exists pe 1 oe such that the hilbert transform is continuous from lp r x into itself

wave number domain separation of the incident and scattered sound field in cartesian and cylindrical coordinates two surface cartesian coordinate system and cylindrical coordinate system measurement techniques are applied to obtain the scattered sound fields of a general shape this decomposition method is based on the principle that any waveform can be decomposed using a two dimensional spatial fourier transform into wave components that propagate in a known manner the cartesian method was developed by tamara j acoust soc am 88 2259 2264 1990 to measure the reflection coefficients of waves incident at oblique angles onto planar surfaces so our paper focuses on the optimization of this method when applied to scattering investigations a two surface technique to separate the incident and scattered field is also developed in cylindrical coordinates the separation process is carried out in the wave number domain in a manner similar to what has been developed for cartesian coordinates however because the incident and scattered fields are not directly separable in cylindrical coordinates knowing general pr

square functions and h calculus on subspaces of l p and on hardy spaces let x be a closed subspace of l p with 1 p and let a be any sectorial operator on x we consider associated square functions on x of the form open image in new window and we show that if a admits a bounded h functional calculus on x then these square functions are equivalent to the original norm of x then we deduce a similar result when x h1 n is the usual hardy space for an appropriate choice of f for example if n 1 the right choice is the sum open image in new window for h h1 where h denotes the hilbert transform

weighted maximal regularity estimates and solvability of non smooth elliptic systems i we develop new solvability methods for divergence form second order real and complex elliptic systems above lipschitz graphs with l 2 boundary data the coefficients a may depend on all

regularization for improving the deconvolution in real time near field acoustic holography near field acoustic holography is a measuring process for locating and characterizing stationary sound sources from measurements made by a microphone array in the near field of the acoustic source plane a technique called real time near field acoustic holography rt nah has been introduced to extend this method in the case of nonstationary sources this technique is based on a formulation which describes the propagation of time dependent sound pressure signals on a forward plane using a convolution product with an impulse response in the time wavenumber domain thus the backward propagation of the pressure field is obtained by deconvolution taking the evanescent waves into account in rt nah improves the spatial resolution of the solution but makes the deconvolution problem ill posed and often yields inappropriate solutions the purpose of this paper is to focus on solving this deconvolution problem two deconvolution methods are compared one uses a singular value decomposition and a standard tikhonov regularization and the other one is based on optimum wiener filtering a simulation involving monopoles driven by nonstationary signals demonstrates by means of objective indicators the accuracy of the time dependent reconstructed sound field the results highlight the advantage of using regularization and particularly in the presence of measurement noise

on subordination of holomorphic semigroups abstract we prove that for any bernstein function the operator a generates a bounded holomorphic c 0 semigroup e t a t 0 on a banach space whenever a does this answers a question posed by kishimoto and robinson moreover giving a positive answer to a question by berg boyadzhiev and de laubenfels we show that e t a t 0 is holomorphic in the holomorphy sector of e t a t 0 and if e t a t 0 is sectorially bounded in this sector then e t a t 0 has the same property we also obtain new sufficient conditions on in order that for every banach space x the semigroup e t a t 0 on x is holomorphic whenever e t a t 0 is a bounded c 0 semigroup on x these conditions improve and generalize well known results by carasso kato and fujita

a numerical approach to degenerate parabolic equations in this work we propose a numerical approach to solve some kind of degenerate parabolic equations the underlying idea is based on the maximum principle more precisely we locally perturb the initial and boundary data instead of the nonlinear diffusion coefficients so that the resulting problem is not degenerate the efficiency of this method is shown analytically as well as numerically the numerical experiments show that this new approach is comparable with the existing ones

a class of asymptotic preserving schemes for the fokker planck landau equation we present a class of asymptotic preserving ap schemes for the nonhomogeneous fokker planck landau nfpl equation filbet and jin 16 designed a class of ap schemes for the classical boltzmann equation by penalization with the bgk operator so they become efficient in the fluid dynamic regime we generalize their idea to the nfpl equation with a different penalization operator the fokker planck operator that can be inverted by the conjugate gradient method we compare the effects of different penalization operators and conclude that the fokker planck fp operator is a good choice such schemes overcome the stiffness of the collision operator in the fluid regime and can capture the fluid dynamic limit without numerically resolving the small knudsen number numerical experiments demonstrate that the schemes possess the ap property for general initial data with numerical accuracy uniformly in the knudsen number

sensitivity of the wave number domain field separation methods for scattering the two surface field separation technique for obtaining the sound field scattered from an object has been shown to be feasible for both the cartesian and cylindrical coordinate systems cheng et al j acout soc am 97 2293 2303 1995 investigations of the sensitivity of implementing these separation techniques to the measurement parameters and their errors will be reported the results of this sensitivity investigation are helpful in deciding the accuracy of the far field target strength results and designing experimental procedures and equipment that ensure accurate results the separation and the spatial processing parameters that are considered include the distance between measurement points in each measurement surface the aperture size of each measurement surface and the distance between measurement surfaces recommendations for these parameters are made next the sensitivity to errors in the experimental geometry is explored for the cartesian coordinate system skew and curvature of the me

convergence of a finite volume scheme for nonlinear degenerate parabolic equations one approximates the entropy weak solution u of a nonlinear parabolic degenerate equation u t rm div mathbf q f u delta phi u 0 by a piecewise constant function u mathcal d using a discretization mathcal d in space and time and a finite volume scheme the convergence of u mathcal d to u is shown as the size of the space and time steps tend to zero in a first step estimates on u mathcal d are used to prove the convergence up to a subsequence of u mathcal d to a measure valued entropy solution called here an entropy process solution a result of uniqueness of the entropy process solution is proved yielding the strong convergence of u mathcal d to it u some on a model equation are shown

approximation of degenerate parabolic problems using numerical integration a class of multidimensional degenerate parabolic equations is considered the two phase stefan problem and the porous medium equation are analyzed as models of singular parabolic equations nonstat

error estimates for a class of degenerate parabolic equations the degenerate parabolic equation u t delta beta u is considered in the cylinder omega times 0 t where omega subset r n is bounded beta 0 beta 0 0 and beta geq0 e g beta u u u m 1 m 1 a fully discrete scheme is given using c0 piecewise linear finite elements in space and a backward difference scheme in time l2 error estimates for the approximation of u and of beta u are proven for that purpose we employ the fact that the free boundary has a finite speed of propagation

method of superposition applied to patch near field acoustic holography the method of superposition may be applied to reconstruct the field on a partial surface on a radiating structure from measurements made on a nearby limited surface unlike conformal near field holography where the measurement surface surrounds the entire structure in patch holography the measurement surface need only be approximately as large as the patch on the structure surface where the reconstruction is required using the method of superposition the field on and near the measurement surface may be approximated by the field produced by a source distribution placed on a surface inside the structure the source strengths are evaluated by applying boundary conditions on the measurement surface the algorithm requires the inversion of the green s function matrix which may be ill conditioned truncated singular value decomposition is used to invert it the field on the structure surface is then approximated by the field produced by the source distribution the algorithm is easier to implement than the

operators with an absolute functional calculus we study sectorial operators with a special type of functional calculus which we term an absolute functional calculus a typical example of such an operator is an invertible operator a defined on a banach space x considered on the real inter polation space dom a x p where 0 1 and 1 p in general the absolute functional calculus can be characterized in terms of real interpolation spaces we show that operators of this type have a strong form of the h calculus and behave very well with respect to the joint functional calculus we give applications of these results to recent work of arendt batty and bu on the existence of holder continuous solutions for the abstract cauchy problem

a posteriori error estimation and adaptivity for degenerate parabolic problems two explicit error representation formulas are derived for degenerate parabolic pdes which are based on evaluating a parabolic residual in negative norms the resulting upper bounds are valid for any numerical method and rely on regularity properties of solutions of a dual parabolic problem in nondivergence form with vanishing diffusion coefficient they are applied to a practical space time discretization consisting of c 0 piecewise linear finite elements over highly graded unstructured meshes and backward finite differences with varying time steps two rigorous a posteriori error estimates are derived for this scheme and used in designing an efficient adaptive algorithm which equidistributes space and time discretization errors via refinement coarsening a simulation finally compares the behavior of the rigorous a posteriori error estimators with a heuristic approach and hints at the potentials and reliability of the proposed method