asymptotic behavior of trajectories for some nonautonomous almost periodic processes abstract in this paper asymptotics are studied for some almost periodic processes on a complete metric space x d 1 it is shown that any precompact positive trajectory of a contractive periodic process is asymptotically almost periodic as t this property does not hold for general almost periodic contractive processes 2 a compactness result is obtained for weakly almost periodic complete trajectories of some possibly nonlinear processes in a uniformly convex banach space 3 the existence of almost periodic trajectories is studied for affine processes in a uniformly convex banach space these results are applicable to some evolution equations of the form du dt a t u t f t where t is almost periodic r v uniformly convex banach space and a t is a periodic time dependent m accretive operator in v

remarks on rates of convergence of powers of contractions abstract we prove that if the numerical range of a hilbert space contraction t is in a certain closed convex set of the unit disk which touches the unit circle only at 1 then t n i t o 1 n with 1 2 1 for normal contractions the condition is also necessary another sufficient condition for 1 2 necessary for t normal is that the numerical range of t be in a disk z z 1 for some 0 1 as a consequence of results of seifert we obtain that a power bounded t on a hilbert space satisfies t n i t o 1 n with 0 1 if and only if sup 1 2 1 1 r t when t is a contraction on l 2 satisfying the numerical range condition it is shown that t n f n 1 converges to 0 a e with a maximal inequality for every f l 2 an example shows that in general a positive contraction t on l 2 may have an f 0 with lim sup t n f log n n a e

strong stability of bounded evolution families and semigroups abstract we prove several characterizations of strong stability of uniformly bounded evolution families u t s t s 0 of bounded operators on a banach space x i e we characterize the property lim t u t s x 0 for all s 0 and all x x these results are connected to the asymptotic stability of the well posed linear nonautonomous cauchy problem u t a t u t t s 0 u s x x x in the autonomous case i e when u t s t t s for some c 0 semigroup t t t 0 we present in addition a range condition on the generator a of t t t 0 which is sufficient for strong stability this condition is more general than the condition in the ablv theorem involving countability of the imaginary part of the spectrum of a

feedbacks for nonautonomous regular linear systems we introduce nonautonomous well posed and absolutely regular linear systems as quadruples consisting of an evolution family and output input and input output maps subject to natural hypotheses in the spirit of weiss work these maps are represented in terms of admissible observation and control operators the latter in an approximate sense in the time domain in this setting the closed loop system exists for a canonical class of admissible feedbacks and it inherits the absolute regularity and other properties of the given system in particular we can iterate feedbacks

implicit high order accurate in space algorithms for the navier stokes equations high order accurate alternating direction implicit schemes have been developed these schemes can be used to obtain efe ciently high resolution numerical solutions of the compressible euler and navier stokes equations implicit solvers compatible with both centered and upwind schemes for the discretization of the convective terms arediscussed forcenteredspacediscretizationoftheconvectivee uxes fourth orderspatialaccuracyoftheimplicit operators is obtained at no additional computing cost by performing compact space differentiation this implicit compact scheme which requires block tridiagonal matrix inversions is used to obtain viscous and inviscid e ow solutions in curvilinear coordinates in addition high order accurate in space implicit operators are obtained for diagonalized schemes which require scalar matrix inversions both high order algorithms improve convergence characteristics for subsonic and transonic e ow compared to second order accurate in space implicit schemes high order accurate in space implicit algorithms compatible with upwind high resolution shock capturing total variation diminishing schemes are also developed third order accurate upwind biased diagonalized algorithms were found to be as accurate and more efe cient than the standard block tridiagonal implicit solvers

on the solution of the minimal rational interpolation problem it is shown that the reachability and the observability indices of appropriately defined pairs of matrices provide the key for solving the minimal rational bitangen tial interpolation problem

growth orders and ergodicity for absolutely cesaro bounded operators abstract in this paper we extend the concept of absolutely cesaro boundedness to the fractional case we construct a weighted shift operator belonging to this class of operators and we prove that if t is an absolutely cesaro bounded operator of order with 0 1 then t n o n generalizing the result obtained for 1 moreover if 1 then t n o n we apply such results to get stability properties for the cesaro means of bounded operators

tauberian theorems and stability of one parameter semigroups the main result is the following stability theorem let t t t tzo be a bounded co semigroup on a reflexive space x denote by a the generator of t and by a a the spectrum of a if a a n ir is countable and no eigenvalue of a lies on the imaginary axis then limt boo t t x o for all x e x

unique recovery of lower order coefficients for hyperbolic equations from data on disjoint sets abstract we consider a restricted dirichlet to neumann map s r t associated with the operator t 2 g a q where g is the laplace beltrami operator of a riemannian manifold m g and a and q are a vector field and a function on m the restriction s r t corresponds to the case where the dirichlet traces are supported on 0 t s and the neumann traces are restricted on 0 t r here s and r are open sets which may be disjoint on the boundary of m we show that s r t determines uniquely up the natural gauge invariance the lower order terms a and q in a neighborhood of the set r assuming that r is strictly convex and that the wave equation is exactly controllable from s in time t 2 we give also a global result under a convex foliation condition the main novelty is the recovery of a and q when the sets r and s are disjoint we allow a and q to be non self adjoint and in particular the corresponding physical system may have dissipation of energy

dissipative operators on banach spaces a bounded linear operator t on a banach space is said to be dissipative if ett 1 for all t 0 we show that if t is a dissipative operator on a banach space then a limt ettt sup t ir b if t ir is contained in i 2 i 2 then limt ettsint sup sin t ir some related problems are also discussed

comparison of implicit schemes for the incompressible navier stokes equations for a computational flow simulation tool to be useful in a design environment it must be very robust and efficient to develop such a tool for incompressible flow applications a number of different implicit schemes are compared for several two dimensional flow problems in the current study the schemes include point jacobi relaxation gauss seidel line relaxation incomplete lower upper decomposition and the generalized minimum residual method preconditioned with each of the three other schemes the efficiency of the schemes is measured in terms of the computing time required to obtain a steady state solution for the laminar flow over a backward facing step the flow over a naca 4412 airfoil and the flow over a three element airfoil using overset grids the flow solver used in the study is the ins2d code that solves the incompressible navier stokes equations using the method of artificial compressibility and upwind differencing of the convective terms the results show that the generalized minimum residual method preconditioned with the incomplete lower upper factorization outperforms all other methods by at least a factor of 2

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

sharp observability estimates for heat equations the goal of this article is to derive new estimates for the cost of observability of heat equations we have developed a new method allowing one to show that when the corresponding wave equation is observable the heat equation is also observable this method allows one to describe the explicit dependence of the observability constant on the geometry of the problem the domain in which the heat process evolves and the observation subdomain we show that our estimate is sharp in some cases particularly in one space dimension and in the multi dimensional radially symmetric case our result extends those in fattorini and russell arch rational mech anal 43 272 292 1971 to the multi dimensional setting and improves those available in the literature namely those by miller j differ equ 204 1 202 226 2004 siam j control optim 45 2 762 772 2006 atti accad naz lincei cl sci fis mat natur rend lincei 9 mat appl 17 4 351 366 2006 and tenenbaum and tucsnak j differ equ 243 1 70 100 2007 our approach is based on an explicit representation formula of some solutions of the wave equation in terms of those of the heat equation in contrast to the standard application of transmutation methods which uses a reverse representation of the heat solution in terms of the wave one we shall also explain how our approach applies and yields some new estimates on the cost of observability in the particular case of the unit square observed from one side we will also comment on the applications of our techniques to controllability properties of heat type equations

model reduction by moment matching for linear and nonlinear systems the model reduction problem for single input single output linear and nonlinear systems is addressed using the notion of moment a re visitation of the linear theory allows to obtain novel results for linear systems and to develop a nonlinear enhancement of the notion of moment this in turn is used to pose and solve the model reduction problem by moment matching for nonlinear systems to develop a notion of frequency response for nonlinear systems and to solve model reduction problems in the presence of constraints on the reduced model connections between the proposed results projection methods the covariance extension problem and interpolation theory are presented finally the theory is illustrated by means of simple worked out examples and case studies

iterates of markov operators and their limits abstract it is well known that iterates of quasi compact operators converge towards a spectral projection whereas the explicit construction of the limiting operator is in general hard to obtain here we show a simple method to explicitly construct this projection operator provided that the fixed points of the operator and its adjoint are known which is often the case for operators used in approximation theory we use an approach related to riesz schauder and fredholm theory to analyze the iterates of operators on general banach spaces while our main result remains applicable without specific knowledge on the underlying framework applications for markov operators on the space of continuous functions c x are provided where x is a compact hausdorff space

on the spectrum of positive linear operators with a partition of unity property abstract we characterize the spectrum of positive linear operators between banach function spaces having finite rank and a partition of unity property our main result states that all the points in the spectrum are eigenvalues and 1 is the only eigenvalue on the unit circle finally we show that the iterates converge in the uniform operator topology to a projection operator that reproduces constant functions and we provide a simple criterion to obtain the limiting projection operator

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

spectral conditions for admissibility and observability of wave systems applications to finite element schemes in this article we derive uniform admissibility and observability properties for the finite element space semi discretizations of ddot u a 0 u 0 where a 0 is an unbounded self adjoint positive definite operator with compact resolvent to address this problem we present a new spectral approach based on several spectral criteria for admissibility and observability of such systems our approach provides very general admissibility and observability results for finite element approximation schemes of ddot u a 0 u 0 which stand in any dimension and for any regular mesh in the sense of finite elements our results can be combined with previous works to derive admissibility and observability properties for full discretizations of ddot u a 0 u 0 we also present applications of our results to controllability and stabilization problems

the stability of numerical boundary treatments for compact high order finite difference schemes the stability characteristics of various compact fourth and sixth order spatial operators are assessed with the theory of gustafsson kreiss and sundstrom g k s for the semidiscrete initial boundary value problem these results are generalized to the fully discrete case with a recently developed theory of kreiss and wu in all cases favorable comparisons are obtained between g k s theory eigenvalue determination and numerical simulation the conventional definition of stability then is sharpened to include only those spatial discretizations that are asymptotically stable bounded left half plane eigenvalues many of the higher order schemes that are g k s stable are not asymptotically stable a series of compact fourth and sixth order schemes that are both asymptotically and g k s stable for the scalar case are then developed

a spillover phenomenon in the optimal location of actuators in this paper we are interested in finding the optimal location and shape of the actuators in a stabilization problem namely we consider the one dimensional wave equation damped by an internal feedback supported on a subdomain omega of given length the criterion we want to optimize represents the rate of decay of the total energy of the system it theoretically involves all the eigenmodes of the operator from an engineering point of view it seems more realistic to consider only a finite number of modes say the n first ones in that context we are able to prove existence and uniqueness of an optimal domain omega n it is the better possible location for the actuators we characterize this optimal domain and we point out the following strange phenomenon at least for small lengths the optimal domain omega n which is the better one for the n first modes is actually the worse one for the n 1th mode this looks like the well known spillover phenomenon in control theory at last we will give some possible extension and open problems in higher dimension

controllability of the linear one dimensional wave equation with inner moving forces we address the null inner controllability of the one dimensional wave equation with supports of the controls that may vary with respect to the time variable we consider theoretical and numerical aspects assuming a geometric optic condition on the support of the controls we first prove a generalized observability inequality for the homogeneous wave equation implying the controllability we then introduce and prove the well posedness of a mixed formulation that characterizes the controls of minimal square integrable norm a numerical approximation of this formulation based on a conformal space time finite element method is then presented several numerical experiments are finally reported

distributed source identification for wave equations an offline observer based approach in this paper we consider the 1 d wave equation where the spatial domain is a bounded interval assuming the initial conditions to be known we are here interested in identifying an unknown source term while we take the neumann derivative of the solution on one of the boundaries as the measurement output applying a back and forth iterative scheme and constructing well chosen observers that will be applied in an offline manner we retrieve the source term from the measurement output in the minimal observation time

the asymptotic lift of a completely positive map starting with a unit preserving normal completely positive map l m m acting on a von neumann algebra or more generally a dual operator system we show that there is a unique reversible system n n i e a complete order automorphism of a dual operator system n that captures all of the asymptotic behavior of l called the asymptotic lift of l this provides a noncommutative generalization of the frobenius theorems that describe the asymptotic behavior of the sequence of powers of a stochastic n n matrix in cases where m is a von neumann algebra the asymptotic lift is shown to be a w dynamical system n z and we identify n z as the tail flow of the minimal dilation of l we are also able to identify the poisson boundary of l as the fixed algebra n in general we show the action of the asymptotic lift is trivial iff l is slowly oscillating in the sense that limn ln 1 ln 0 m hence is often a nontrivial automorphism of n the asymptotic lift of a variety of examples is calculated

optimal hankel model reduction for nonminimal systems a basis free descriptor system representation is shown to facilitate the computation of all minimum degree and optimal kth order all pass extensions and hankel norm approximants the descriptor representation has the same simple form for both the optimal and suboptimal cases the method makes hankel model reduction practical for nonminimal and nearly nonminimal systems by eliminating the ill conditioned calculation of a minimal balanced realization a simple numerically sound method based on singular value decomposition enables the results to be expressed in state space form

comparable upper and lower bounds for boundary values of neumann eigenfunctions and tight inclusion of eigenvalues for smooth bounded domains in rn we prove upper and lower l2 bounds on the boundary data of neumann eigenfunctions and we prove quasiorthogonality of this boundary data in a spectral window the bounds are tight in the sense that both are independent of the eigenvalues this is achieved by working with an appropriate norm for boundary functions which includes a spectral weight that is a function of the boundary laplacian this spectral weight is chosen to cancel concentration at the boundary that can happen for whispering gallery type eigenfunctions these bounds are closely related to wave equation estimates due to tataru using this we bound the distance from an arbitrary helmholtz parameter e 0 to the nearest neumann eigenvalue in terms of boundary normal derivative data of a trial function u solving the helmholtz equation e u 0 this inclusion bound improves over previously known bounds by a factor of e5 6 analogously to a recently improved inclusion bound in the dirichlet case due to the first two authors finally we apply our theory to present an improved numerical implementation of the method of particular solutions for computation of neumann eigenpairs on smooth planar domains we show that the new inclusion bound improves the relative accuracy in a computed neumann eigenvalue around the 42000th from nine to fourteen digits with negligible extra numerical effort

theorems of katznelson tzafriri type for contractions for t a contraction on a hilbert space and a function in the disc algebra we show that if 0 on spt then limn t tn 0 the same method gives a new proof of recent results of katznelson tzafriri several applications are given

artificial dissipation models for the euler equations various artificial dissipation models that are used with central difference algorithms for the euler equations are analyzed for their effect on accuracy stability and convergence rates in particular linear and nonlinear models are investigated using an implicit approximate factorization code arc2d for transonic airfoils fully implicit application of the dissipation models is shown to improve robustness and convergence rates the treatment of dissipation models at boundaries will be examined it will be shown that accurate error free solutions with sharp shocks can be obtained using a central difference algorithm coupled with an appropriate nonlinear artificial dissipation model i introduction t he solution of the euler equations using numerical techniques requires the use of either a differencing method with inherent dissipation or the addition of dissipation terms to a nondissipative scheme this is because the euler equations do not provide any natural dissipation mechanism such as viscosity in the navier stokes equations that would eliminate high frequencies which are caused by nonlinearitie s and especially shocks a variety of numerical algorithms and computer codes for the euler equations have been developed methods such as maccormack s1 explicit

a family of high order finite difference schemes with good spectral resolution this paper presents a family of finite difference schemes for the first and second derivatives of smooth functions the schemes are hermitian and symmetric and may be considered a more general version of the standard compact pade schemes discussed by lele they are different from the standard pade schemes in that the first and second derivatives are evaluated simultaneously for the same stencil width the proposed schemes are two orders higher in accuracy and have significantly better spectral representation eigenvalue analysis and numerical solutions of the one dimensional advection equation are used to demonstrate the numerical stability of the schemes the computational cost of computing both derivatives is assessed and shown to be essentially the same as the standard pade schemes the proposed schemes appear to be attractive alternatives to the standard pade schemes for computations of the navier stokes equations

some results of katznelson tzafriri type abstract for semigroups s r z and z k we show that if t is a representation of s by contractions on a hilbert space then inf t s t t f t sup f sp u t s where f l 1 s and sp u t s is the unitary spectrum of t with respect to s for t a representation of a suitable semigroup s by contractions on a banach space we give sharp conditions on sp u t s which guarantee that the equality above holds these conditions concern the thinness of sp u t s in the harmonic analysis sense these results are related to theorems of katznelson tzafriri type which give conditions guaranteeing that inf t s t t f t vanishes

a generalization of sectorial and quasi sectorial operators abstract in the paper we generalize the main results presented in bentkus and paulauskas 2004 2 by giving rates of approximation of some semigroups of operators of the order n 0 1 also two classes of operators generalizing sectorial and quasi sectorial operators are introduced and their properties are studied

theorems of katznelson tzafriri type for semigroups of operators let s be a locally compact abelian semigroup and t a bounded representation of s by linear bounded operators in a banach space x with spectrum sp t let spu t be the intersection of sp t with the set of unitary characters of s we prove that if s r or if t is norm continuous and if f is a function in l1 s which is of spectral synthesis with respect to spu t then inft s sf s t t s ds 0

computation of oscillating airfoil flows with one and two equation turbulence models the ability of one and two quation turbulence models to predict unsteady separated flows over airfoils is evaluated an implicit factorized upwind biased numerical scheme is used for the integration of the compressible reynolds averaged navier stokes equations the turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations one and two equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence the same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic mach numbers experimental cases where the flow has been tripped at the leading edge and where natural transition was allowed to occur naturally are considered the more recently developed turbulence models capture the physics of unsteady separated flow significantly better than the standard k e and k models however certain differences in the hysteresis effects are observed for an untripped high reynolds number flow it was found necessary to take into account the leading edge transitional flow region to capture the correct physical mechanism that leads to dynamic stall

stability and almost periodicity of trajectories of periodic processes abstract we prove that if the monodromy operator v of a linear periodic process u t in a banach space e is power bounded has countable peripheral spectrum and if its peripheral point spectrum satisfies a certain natural and simple duality condition which always holds in reflexive spaces then every positive trajectory u u 0 x 0 x e is asymptotically almost periodic if in particular the peripheral point spectrum of v is empty then every positive trajectory is asymptotically stable we also obtain results on almost periodicity of complete bounded trajectories and consider conditions under which nontrivial complete trajectories exist

model reduction of neutral linear and nonlinear time invariant time delay systems with discrete and distributed delays the problem of model reduction by moment matching for linear and nonlinear differential time delay systems is studied the class of models considered includes neutral differential time delay systems with discrete delays and distributed delays the description of moment is revisited by means of a sylvester like equation for linear time delay systems and by means of the center manifold theory for nonlinear time delay systems in addition the moments at infinity are characterized for both linear and nonlinear time delay systems parameterized families of models achieving moment matching are given the parameters can be exploited to derive delay free reduced order models or time delay reduced order models with additional properties e g interpolation at an arbitrary large number of points finally the problem of obtaining a reduced order model of an unstable system is discussed and solved

exponential decay of energy of evolution equations with locally distributed damping consider an evolution equation with energy dissipation frac partial partial t y x t ay x t by x t on a bounded x domain omega where by signifies a dissipative perturbation to an otherwise energy conserving system this dissipation may be due to medium impurities viscous effects or artificially imposed dampers and stabilizers it is distributed over only part of the domain omega the question of when the dissipation is effective enough to cause uniform exponential decay of energy is examined because of the locally distributed nature of energy dissipation the problem lacks coercivity and is not directly solvable by energy identities thus to get conditions sufficient for uniform exponential decay a different approach needs to be taken provided here is a set of tight sufficient conditions in terms of the influence of the dissipative operatorbon the separated eigenmodes or clustered eigenmodes ofa the main theorems are general enough to treat the wave and bea

an easily implementable fourth order method for the time integration of wave problems abstract we are concerned with the time integration of systems of ordinary differential equations arising from the space discretization of partial differential wave equations with smooth solutions a method is suggested that while being as easily implementable as the standard implicit mid point rule is fourth order accurate the new method is symplectic so that it is very well suited for long time integrations of problems with a hamiltonian structure numerical experiments are reported that refer to a fourth order galerkin space discretization of the korteweg de vries equation and to a pseudospectral space discretization of the same equation

moments of random variables a systems theoretic interpretation moments of continuous random variables admitting a probability density function are studied we show that under certain assumptions the moments of a random variable can be characterized in terms of a sylvester equation and of the steady state output response of a specific interconnected system this allows to interpret well known notions and results of probability theory and statistics in the language of systems theory including the sum of independent random variables the notion of mixture distribution and results from renewal theory the theory developed is based on tools from center manifold theory the theory of the steady state response of nonlinear systems and the theory of output regulation our formalism is illustrated by means of several examples and can be easily adapted to the case of discrete and multivariate random variables

fractional balanced reduction model reduction via fractional representation a method for the model reduction of finite dimensional linear time invariant fdlti plants is proposed which uses normalized fractional representations is proposed the method dubbed fractional balanced reduction applies balance and truncate to a special representation of the graph operator of the plant this operation yields the graph operator of a reduced order plant the method has such properties as existence of an a priori error bound in the graph metric and preservation of sector containment coupling fractional representations with principal component analysis gives a model reduction method that is capable of producing in a numerically stable way a good reduced order model using the whole full order model sector properties are also preserved these are useful for deciding stability when nonlinearities are in the loop

implicit method for the computation of unsteady flows on unstructured grids an implicit method for the computation of unsteady flows on unstructured grids is presented following a finite difference approximation for the time derivative the resulting nonlinear system of equations is solved at each time step by using an agglomeration multigrid procedure the method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage inviscid and viscous unsteady flows are computed to validate the procedure the issue of the mass matrix which arises with vertex centered finite volume schemes is addressed the present formulation allows the mass matrix to be inverted indirectly a mesh point movement and reconnection procedure is described that allows the grids to evolve with the motion of bodies as an example of flow over bodies in relative motion flow over a multi element airfoil system undergoing deployment is computed

the modulus of a regular linear operator and the zero two law in lp spaces 1 p p 2 abstract using the linear modulus of a regular operator we extend the zero two law for positive contractions of l p spaces 1 p p 2 the proof uses the approximate point spectrum of positive contractions and a procedure obtained by foguel

growth order and stability of discrete semigroups abstract characterizations of the growth order and the stability for the orbit t n x of the powers t n of a bounded linear operator t in terms of cesaro and abel means of the orbit are obtained it is also seen that under the tauberian condition n t n 1 t n o 1 the strong resp uniform convergence of t n is equivalent to its strong resp uniform abel mean convergence

uniform monotonicity of norms and the strong zero two law abstract recently rainer wittmann proved a strong zero two law for positive contractions of lp spaces 1 p

explicit and implicit multidimensional compact high resolution shock capturing methods two families of explicit and implicit compact high resolution shock capturing methods for the multidimensional compressible euler equations for fluid dynamics are constructed some of these schemes can be fourth and sixth order accurate away from discontinuities for the semi discrete case their shock capturing properties are of the total variation diminishing tvd total variation bounded tvb total variation diminishing in the mean tvdm essentially nonoscillatory eno or positive type of scheme for 1d scalar hyperbolic conservation laws and are positive schemes in more than one dimension these higher order compact schemes require the same grid stencil per spatial direction as their second order noncompact cousins the added terms over the second order noncompact cousins involve extra vector additions but no added flux evaluations due to the construction these schemes can be viewed as approximations to genuinely multidimensional schemes in the sense that they might produce less distortion in spherical type shocks and are more accurate in vortex type flows than schemes based purely on 1d extensions the extension of these families of compact schemes to coupled nonlinear systems can be accomplished using the roe approximate riemann solver the generalized steger and warming flux vector splitting or the van leer type flux vector splitting modification to existing high resolution second or third order noncompact shock capturing computer codes is minimal high resolution shock capturing properties can also be achieved via a variant of the second order lax friedrichs numerical flux without the use of riemann solvers for coupled nonlinear systems with comparable operations count to their classical shock capturing counterparts an efficient and compatible high resolution shock capturing filter for spatially fourth and sixth order classical compact and noncompact schemes is discussed the simplest extension to viscous flows can be achieved by using the standard fourth order compact or noncompact formula for the viscous terms

asymptotics for periodic systems abstract this paper investigates the asymptotic behaviour of solutions of periodic evolution equations starting with a general result concerning the quantified asymptotic behaviour of periodic evolution families we go on to consider a special class of dissipative systems arising naturally in applications for this class of systems we analyse in detail the spectral properties of the associated monodromy operator showing in particular that it is a so called ritt operator under a natural resonance condition this allows us to deduce from our general result a precise description of the asymptotic behaviour of the corresponding solutions in particular we present conditions for rational rates of convergence to periodic solutions in the case where the convergence fails to be uniformly exponential we illustrate our general results by applying them to concrete problems including the one dimensional wave equation with periodic damping

tauberian theorems for the laplace stieltjes transform let a 0 oo c be a function of locally bounded variation with a 0 0 whose laplace stieltjes transform g z fo e z da t is absolutely convergent for re z 0 let e be the singular set of g in ir and suppose that 0 e various estimates for lim supt la t g o l are obtained in particular a t g 0 as t oo if i e is null ii sup sup e aysda s oo yee t o o iii lim lim sup sup a s a t 0 610 t oo t 6 s t this result contains tauberian theorems for laplace transforms power series and dirichlet series

sharp sufficient conditions for the observation control and stabilization of waves from the boundary for the observation or control of solutions of second order hyperbolic equation in mathbb r t times omega ralston s construction of localized states comm pure appl math 22 1969 pp

stabilization and control for the nonlinear schrodinger equation on a compact surface in this paper we study the stabilization property and the exact controllability for the nonlinear schrodinger equation on a two dimensional compact riemannian manifold without boundary we use a pseudo differential dissipation the proofs are based on a result of propagation of singularities and on recent dispersion estimates strichartz type inequalities due to n burq p gerard and n tzvetkov

a generalized entropy criterion for nevanlinna pick interpolation with degree constraint we present a generalized entropy criterion for solving the rational nevanlinna pick problem for n 1 interpolating conditions and the degree of interpolants bounded by n the primal problem of maximizing this entropy gain has a very well behaved dual problem this dual is a convex optimization problem in a finite dimensional space and gives rise to an algorithm for finding all interpolants which are positive real and rational of degree at most n the criterion requires a selection of a monic schur polynomial of degree n it follows that this class of monic polynomials completely parameterizes all such rational interpolants and it therefore provides a set of design parameters for specifying such interpolants the algorithm is implemented in a state space form and applied to several illustrative problems in systems and control namely sensitivity minimization maximal power transfer and spectral estimation

identification of small amplitude perturbations in the electromagnetic parameters from partial dynamic boundary measurements we consider the inverse problem of reconstructing small amplitude perturbations in the conductivity for the wave equation from partial on part of the boundary dynamic boundary measurements through construction of appropriate test functions by a geometrical control method we provide a rigorous derivation of the inverse fourier transform of the perturbations in the conductivity as the leading order of an appropriate averaging of the partial dynamic boundary perturbations this asymptotic formula is generalized to the full time dependent maxwell s equations our formulae may be expected to lead to very effective computational identification algorithms aimed at determining electromagnetic parameters of an object based on partial dynamic boundary measurements

model reduction by matching the steady state response of explicit signal generators model reduction by moment matching for interpolation signals which do not have an implicit model i e they do not satisfy a differential equation is considered particular attention is devoted to discontinuous possibly periodic signals the notion of moment is reformulated using an integral matrix equation it is shown that under specific conditions the new definition and the one based on the sylvester equation are equivalent new parameterized families of models achieving moment matching are given the results are illustrated by means of a numerical example

wigner measures and observability for the schrodinger equation on the disk we analyse the structure of semiclassical and microlocal wigner measures for solutions to the linear schrodinger equation on the disk with dirichlet boundary conditions our approach links the propagation of singularities beyond geometric optics with the completely integrable nature of the billiard in the disk we prove a structure theorem expressing the restriction of the wigner measures on each invariant torus in terms of second microlocal measures they are obtained by performing a finer localization in phase space around each of these tori at the limit of the uncertainty principle and are shown to propagate according to heisenberg equations on the circle our construction yields as corollaries a that the disintegration of the wigner measures is absolutely continuous in the angular variable which is an expression of the dispersive properties of the equation b an observability inequality saying that the l 2 norm of a solution on any open subset intersecting the boundary resp the l 2 norm of the neumann trace on any nonempty open set of the boundary controls its full l 2 norm resp h 1 norm these results show in particular that the energy of solutions cannot concentrate on periodic trajectories of the billiard flow other than the boundary

exponential stability for infinite dimensional non autonomous port hamiltonian systems abstract we study the non autonomous version of an infinite dimensional linear port hamiltonian system on an interval a b employing abstract results on evolution families we show c 1 well posedness of the corresponding cauchy problem and thereby existence and uniqueness of classical solutions for sufficiently regular initial data further we demonstrate that a dissipation condition in the style of the dissipation condition sufficient for uniform exponential stability in the autonomous case also leads to a uniform exponential decay rate of the energy in this non autonomous setting

power boundedness in fourier and fourier stieltjes algebras and other commutative banach algebras abstract we study power boundedness in the fourier and fourier stieltjes algebras a g and b g of a locally compact group g as well as in some other commutative banach algebras the main results concern the question of when all elements with spectral radius at most one in any of these algebras are power bounded the characterization of power bounded elements in a g and b g and also the structure of the gelfand transform of a single power bounded element

a note on stabilization of locally damped wave equations with time delay abstract in this paper we consider the wave equation with internal distributed time delay and local damping in a bounded and smooth domain r n when the local damping acts on a neighborhood of a suitable part of the boundary of we show that an exponential stability result holds if the coefficient of the delay term is sufficiently small

on power bounded operators abstract the main result asserts that for any contraction t on an arbitrary banach space x t n t n 1 0 as n if and only if the spectrum of t has no points on the unit circle except perhaps z 1 this theorem is extended for t t n where is a function of spectral synthesis on the unit circle as an application we generalize the so called zero two law of ornstein and sucheston and zaharopol to positive contraction on a very large class of banach lattices

sylvester equations and projection based model reduction in this paper we establish a connection between krylov subspace techniques for multipoint pade interpolation and the use of sylvester equations for constructing reduced order models we also briefly point out that this connection partly extends to adi type techniques and to the smith iteration for computing approximate solutions of lyapunov equations

almost periodicity of mild solutions of inhomogeneous periodic cauchy problems abstract we consider a mild solution u of a well posed inhomogeneous cauchy problem u t a t u t f t on a banach space x where a is periodic for a problem on r we show that u is asymptotically almost periodic if f is asymptotically almost periodic u is bounded uniformly continuous and totally ergodic and the spectrum of the monodromy operator v contains only countably many points of the unit circle for a problem on r we show that a bounded uniformly continuous solution u is almost periodic if f is almost periodic and various supplementary conditions are satisfied we also show that there is a unique bounded solution subject to certain spectral assumptions on v f and u

multirate modeling and control design for switched mode power converters a class of pulse width modulated pwm systems that includes many switched mode power converters is considered a new multirate low frequency sampling pwm scheme is introduced that not only provides the possibility for new types of operation but also unifies the switching logic corresponding to established pwm schemes an exact nonlinear discrete time model is used to develop multirate nonlinear controllers and observers based on map inversion concepts this nonlinear design methodology is widely applicable requiring only that the continuous time small signal average model be controllable and observable

observability and control of schrodinger equations we propose an exact controllability result for schrodinger equations in bounded domains under the bardos lebeau rauch geometric control condition with an estimate of the control which is explicit with respect to the time of controllability also we prove an explicit in time logarithmic observability estimate for the schrodinger equation where no geometrical conditions are supposed on the domain

tauberian theorems and stability of solutions of the cauchy problem let f r x be a bounded strongly measurable function with values in a banach space x and let ie be the singular set of the laplace transform f in ir suppose that e is countable and 0 e i uf s u du 0 uniformly for s 0 as 0 for each in e it is shown that t 0 e i uf u du f i 0 as t for each in r e in particular f t 0 if f is uniformly continuous this result is similar to a tauberian theorem of arendt and batty it is obtained by applying a result of the authors concerning local stability of bounded semigroups to the translation semigroup on buc r x and it implies several results concerning stability of solutions of cauchy problems

remarks on the asymptotic behavior of the solution to damped wave equations abstract we study the diffusion phenomena for damped wave equations we prove that the solution of an abstract damped wave equation becomes closer to the solution of a heat type equation as time tends to infinity under some assumption to the resolvent as an application of our approach we also study the asymptotic behavior of the damped wave equation in euclidean space under the geometric control condition

asymptotic stability of the wave equation on compact manifolds and locally distributed damping a sharp result let m g be a n dimensional n geqq 2 compact riemannian manifold with boundary where g denotes a riemannian metric of class c this paper is concerned with the study of the wave equation on m g with locally distributed damping described by left begin array l u tt delta bf g u a x g u t 0 quad hbox on thinspace m times left 0 infty right u 0 hbox on partial m times left 0 infty right end array right where m represents the boundary of m and a x g ut is the damping term the main goal of the present manuscript is to generalize our previous result in cavalcanti et al trans ams 361 9 4561 4580 2009 treating the conjecture in a more general setting and extending the result for n dimensional compact riemannian manifolds m g with boundary in two ways i by reducing arbitrarily the region m ast subset m where the dissipative effect lies this gives us a totally sharp result with respect to the boundary measure and interior measure where the damping is effective ii by controlling the existence of subsets on the manifold that can be left without any dissipative mechanism namely a precise part of radially symmetric subsets an analogous result holds for compact riemannian manifolds without boundary

a new flux vector splitting compact finite volume scheme a new high resolution finite volume method is proposed here that uses flux vector splitting as the building block to represent the physical processes the high accuracy projection in space is obtained here inter alia by using some compact schemes of sengupta et al 1 and lele 2 that have extremely high accuracy in spectral plane this produces a new class of finite volume fv scheme for spatial discretization that has been analyzed for spectral accuracy numerical stability and dispersion relation preservation drp property following the full domain analysis method of 1 using two different time integration strategies these combination of spatial and temporal methods have been tested for two linear wave problems reported in 1 3 and the solution of burgers equation is compared with the analytical results presented in adams and shariff 4 the shock capturing method is based on the proposed technique in 5 that does not require the usage of any nonlinear differencing techniques or limiters to show that the proposed method can also handle irregular grids the burgers equation is solved using non uniform grids also to demonstrate the utility of the proposed scheme to solve practical problems the benchmark problem of nonlinear wave propagation in a one dimensional shock tube has been solved with the initial data as given in 23 by solving the euler equation the analysis and comparison of this flux vector splitting scheme with other well known methods clearly demonstrate the superior scale resolution of the proposed method at the same time providing a neutrally stable scheme when used with four stage runge kutta scheme also the same scheme displays extended ranges of wave numbers and circular frequencies over which drp property is valid the computed results of three test cases and their comparison with analytical results clearly reveal that the presented method can be used for practical problems

explicit observability inequalities for the wave equation with lower order terms by means of carleman inequalities in this paper by means of carleman estimates and the usual energy estimate we obtain directly two observability inequalities for the linear wave equation with time variant nonsmooth lower order terms we do not need any unique continuation property of the linear equation a priori since this is actually one of the by products of our analysis furthermore the constant in the observability inequality is estimated by an explicit function of the norm of the involved coefficients in the equation also we apply our observability estimates to exact controllability for wave equations

null controllability of a system of linear thermoelasticity we consider a linear system of thermoelasticity in a compact c infin n dimensional connected riemannian manifold this system consists of a wave equation coupled to a heat equation when the boundary of the manifold is non empty dirichlet boundary conditions are considered we study the controllability properties of this system when the control acts in the hyperbolic equation and not in the parabolic one and has its support restricted to an open subset of the manifold we show that if the control time and the support of the control satisfy the geometric control condition for the wave equation this system of thermoelasticity is null controllable more precisely any finite energy solution can be driven to zero at the control time an analogous result is proved when the control acts on the parabolic equation finally when the manifold has no boundary the null controllability of the linear system of three dimensional thermoelastic ity is proved

resolvent conditions and growth of powers of operators abstract following bermudez et al 5 we study the rate of growth of the norms of the powers of a linear operator under various resolvent conditions or cesaro boundedness assumptions in hilbert spaces we prove that if t satisfies the kreiss condition t n o n log n if t is absolutely cesaro bounded t n o n 1 2 e for some e 0 which depends on t if t is strongly kreiss bounded then t n o log n for some 0 we show that a kreiss bounded operator on a reflexive space is abel ergodic and its cesaro means of order converge strongly when 1

fast and strongly localized observation for the schrodinger equation we study the exact observability of systems governed by the schrodinger equation in a rectangle with homogeneous dirichlet respectively neumann boundary conditions and with neumann respectively dirichlet boundary observation generalizing previous results of ramdani takahashi tenenbaum and tucsnak we prove that these systems are exactly observable in arbitrarily small time moreover we show that the above results hold even if the observation regions have arbitrarily small measures more precisely we prove that in the case of homogeneous neumann boundary conditions with dirichlet boundary observation the exact observability property holds for every observation region whith non empty interior in the case of homogeneous dirichlet boundary conditions with neumann boundary observation we show that the exact observability property holds if and only if the observation region has an open intersection with an edge of each direction moreover we give explicit estimates for the blow up rate of the observability constants as the time and or the size of the observation region tend to zero the main ingredients of the proofs are an effective version of a theorem of beurling and kahane on non harmonic fourier series and an estimate for the number of lattice points in the neighbourhood of an ellipse

optimal rates of decay in the katznelson tzafriri theorem for operators on hilbert spaces abstract the katznelson tzafriri theorem is a central result in the asymptotic theory of discrete operator semigroups it states that for a power bounded operator t on a banach space we have t n i t 0 if and only if t t 1 the main result of the present paper gives a sharp estimate for the rate at which this decay occurs for operators on hilbert space assuming the growth of the resolvent norms r e i t as 0 satisfies a mild regularity condition this significantly extends an earlier result by the second author which covered the important case of polynomial resolvent growth we further show that under a natural additional assumption our condition on the resolvent growth is not only sufficient but also necessary for the conclusion of our main result to hold by considering a suitable class of toeplitz operators we show that our theory has natural applications even beyond the setting of normal operators for which we in addition obtain a more general result