strong stability of an unstable wave equation by boundary feedback with only displacement observation the stabilization of a 1 d wave equation that contains instability at its free end and control at the other end is considered the controller is designed through the estimated state that is designed in the case that only displacement is available the method of backstepping is adopted in investigation the c0 semigroup theory and lyapunov method are used to show that the closed loop system is asymptotically stable

uniform stabilization of wave equation with localized damping and acoustic boundary condition abstract in this paper we deal with stability of the nonlinear wave equation with acoustic boundary conditions to non locally reacting boundary

approximation of pseudodifferential operators in absorbing boundary conditions for hyperbolic equations engquist and majda 3 proposed a pseudodifferential operator as asymptotically valid absorbing boundary condition for hyperbolic equations in the case of the wave equation this boundary condition is valid at all frequencies here least squares approximation of the symbol of the pseudodifferential operator is proposed to obtain differential operators as boundary conditions it is shown that for the wave equation this approach leads to kreiss well posed initial boundary value problems and that the expectation of the reflected energy is lower than in the case of taylor and pade approximations 3 4 numerical examples indicate that this method works even more effectively for hyperbolic systems the least squares approach may be used to generate the boundary conditions automatically

an aggregate subgradient method for nonsmooth convex minimization a class of implementable algorithms is described for minimizing any convex not necessarily differentiable functionf of several variables the methods require only the calculation off and one subgradient off at designated points they generalize lemarechal s bundle method more specifically instead of using all previously computed subgradients in search direction finding subproblems that are quadratic programming problems the methods use an aggregate subgradient which is recursively updated as the algorithms proceed each algorithm yields a minimizing sequence of points and iff has any minimizers then this sequence converges to a solution of the problem particular members of this algorithm class terminate whenf is piecewise linear the methods are easy to implement and have flexible storage requirements and computational effort per iteration that can be controlled by a user

absorbing boundary conditions for difference approximations to the multi dimensional wave equation construction des conditions aux limites absorbantes pour l equation des ondes multidimensionnelle a l aide d approximations aux differences formulation sous forme canonique des conditions aux limites absorbantes analytiques

local optimization based simplicial mesh untangling and improvement we present an optimization based approach for mesh untangling that maximizes the minimum area or volume of simplicial elements in a local submesh these functions are linear with respect to the free vertex position thus the problem can be formulated as a linear program that is solved by using the computationally inexpensive simplex method we prove that the function level sets are convex regardless of the position of the free vertex and hence the local subproblem is guaranteed to converge maximizing the minimum area or volume of mesh elements although well suited for mesh untangling is not ideal for mesh improvement and its use often results in poor quality meshes we therefore combine the mesh untangling technique with optimization based mesh improvement techniques and expand previous results to show that a commonly used two dimensional mesh quality criterion can be guaranteed to converge when starting with a valid mesh typical results showing the effectiveness of the combined untangling and smoothing techniques are given for both two and three dimensional simplicial meshes

on the exponential decay in thermoelasticity without energy dissipation and of type iii in presence of an absorbing boundary we study the asymptotic behavior of the solution of a 3d hyperbolic system arising in the green naghdi models of thermoelasticity of type ii and iii with a dissipative boundary condition for the displacement and prove that the energy exponentially decays in time

global existence and uniform decay for wave equation with dissipative term and boundary damping in this paper we prove the existence uniqueness and uniform stability of strong and weak solutions of the nonlinear wave equation u t email protected b x u t f u 0 in bounded domains with nonlinear damped boundary conditions given by email protected email protected g u t 0 with restrictions on function f u g u t and b x we prove the existence by means of the glerkin method and obtain the asymptotic behavior by using of the multiplier technique from the idea of kmornik and zuazua see 7

resonance modes in a one dimensional medium with two purely resistive boundaries calculation methods orthogonality and completeness studying the problem of wave propagation in media with resistive boundaries can be made by searching for resonance modes or free oscillations regimes in the present article a simple case is investigated which allows one to enlighten the respective interest of different classical methods some of them being rather delicate this case is the one dimensional propagation in a homogeneous medium having two purely resistive terminations the calculation of the green function being done without any approximation using three methods the first one is the straightforward use of the closed form solution in the frequency domain and the residue calculus then the method of separation of variables space and time leads to a solution depending on the initial conditions the question of the orthogonality and completeness of the complex valued resonance modes is investigated leading to the expression of a particular scalar product the last method is the expansion in biorthogonal modes in the frequency domain the modes having eigenfrequencies depending on the frequency results of the three methods generalize or and correct some results already existing in the literature and exhibit the particular difficulty of the treatment of the constant mode

a dynamic control law for the wave equation abstract we consider a system described by the one dimensional linear wave equation in a bounded domain with appropriate boundary conditions to stabilize the system we propose a dynamic boundary controller applied at the free end of the system the transfer function of the proposed controller is restricted to be a positive real function which could be strictly proper we then show that if the transfer function of the controller is strictly proper then the resulting closed loop system is asymptotically stable and if proper but not strictly proper then the resulting closed loop system is exponentially stable

stabilization of hyperbolic and parabolic systems with nonlinearly perturbed boundary conditions abstract sufficient conditions for the local exponential stabilizability of abstract systems described by an arbitrary co semigroup with nonlinear unbounded perturbations are formulated applications to parabolic and in particular hyperbolic problems with nonlinearity appearing in the boundary conditions are given

reservoir characterization using stochastic initializations and the level set method in this work we present a novel level set technique for shape reconstruction in history matching for reservoirs with two or more kinds of rocks the so called lithofacies using stochastic initializations in the paper we discuss the use of sequential gaussian simulation for the creation of geostatistical initial guesses which will then be applied to an earlier introduced level set based shape reconstruction algorithm for the history matching problem in reservoir characterization the shapes or regions with sharp interfaces to each other are represented by a level set function which needs to be determined from the production data gathered at few locations of the reservoir we present numerical results in 2d which demonstrate that our method is able to provide reliable estimates of this structure from these relatively few production data even though the topology of the unknown regions is a priori unknown

upper bounds on codes correcting asymmetric errors corresp a survey is given of known upper bounds on codes correcting asymmetric errors the bounds are improved by introducing new ideas by solving a linear programming problem an upper bound is given that is easy to compute for all codelengths and all minimum asymmetric distances

untangling of 2d meshes in ale simulations a procedure is presented to untangle unstructured 2d meshes containing inverted elements by node repositioning the inverted elements may result from node movement in arbitrary lagrangian eulerian ale simulations of continuum mechanics problems with large shear deformation such as fluid flow and metal forming meshes with inverted elements may also be created due to the limitations of mesh generation algorithms particularly for nonsimplicial mesh generation the untangling procedure uses a combination of direct node placement based on geometric computation of the feasible set and node repositioning driven by numerical optimization of an objective function that achieves its minimum on a valid mesh it is shown that a combination of the feasible set based method and the optimization method achieves the best results in untangling complex 2d meshes preliminary results are also presented for untangling of 3d unstructured meshes by the same approach

stabilization of hyperbolic systems using concentrated sensors and actuators certain hyperbolic systems of partial differential equations which are known to be uniformly asymptotically stabilizable using point sensors actuators s a are considered the issue to be investigated is the effect on stability when point s a s are replaced by concentrated s a s that is s a s which average over small regions of the spatial domain although it is known that passing from point to concentrated s a s necessarily destroys uniform stability a necessary and sufficient condition for strong stability is obtained in terms of the s a weighting functions in addition in the special case of a cantilevered beam controlled by a single sensor actuator pair concentrated at the free end another more robust type of stability is shown to hold even when strong stability does not the latter result shows that the system energy is bounded by a part which goes uniformly to zero at infinity and a residual which can be explicitly estimated in terms of the support of the weight functions and the initial energy furthermore the residual energy converges to zero as the support reduces to the point at the free end of the beam

bounds and constructions for binary asymmetric error correcting codes corresp by use of known bounds on constant weight binary codes new uppper bounds are obtained on the cardinality of binary codes correcting asymmetric errors some constructions are exhibited that come close to these bounds for single error correcting codes some constructions are derived from the steiner system s 5 6 12 and for double error correcting codes some constructions are derived from the nordstrom robinson code

the construction of compatible hydrodynamics algorithms utilizing conservation of total energy the principal goal of all numerical algorithms is to represent as faithfully and accurately as possible the underlying continuum equations to which a numerical solution is sought however in the transformation of the equations of fluid dynamics into discretized form important physical properties are either lost or obeyed only to an approximation that often becomes worse with time this is because the numerical methods used to form the discrete analog of these equations may only represent them to some order of local truncation error without explicit regard to global properties of the continuum system although a finite truncation error is inherent to all discretization methods it is possible to satisfy certain global properties such as conservation of mass momentum and total energy to numerical roundoff error the purpose of this work is to show how these equations can be differenced compatibly so that they obey the aforementioned properties in particular it is shown how conservation of total energy can be utilized as an intermediate device to achieve this goal for the equations of fluid dynamics written in lagrangian form and with a staggered spatial placement of variables for any number of dimensions and in any coordinate system for staggered spatial variables it is shown how the momentum equation and the specific internal energy equation can be derived from each other in a simple and generic manner by use of the conservation of total energy this allows for the specification of forces that can be of an arbitrary complexity such as those derived from an artificial viscosity or subzonal pressures these forces originate only in discrete form nonetheless the change in internal energy caused by them is still completely determined the procedure given here is compared to the method of support operators to which it is closely related difficulties with conservation of momentum volume and entropy are also discussed the proper treatment of boundary conditions and differencing with respect to time are detailed

global exact controllability of a class of quasilinear hyperbolic systems in this paper we consider a distributed parameter boundary control system described by a reducible quasilinear hyperbolic system formula posed on the domain 0 x 1 with the nonlinear boundary conditions formula in the case that the system islinear degenerate we show that it isgloballyexactly boundary controllable

extending sobolev functions with partially vanishing traces from locally e δ domains and applications to mixed boundary problems we prove that given any k n for each open set rn and any closed subset d of such that is locally an e domain near d there exists a linear and bounded extension operator ek d mapping for each p 1 the space wdk p into wdk p rn here with o denoting either or rn the space wdk p o is defined as the completion in the classical sobolev space wk p o of restrictions to o of functions from cc rn whose supports are disjoint from d in turn this result is used to develop a functional analytic theory for the class wdk p including intrinsic characterizations boundary traces and extensions results interpolation theorems among other things which is then employed in the treatment of mixed boundary value problems formulated in locally e domains finally we also prove extension results on the scales of besov and bessel potential spaces on e domains with partially vanishing traces on ahlfors regular sets and explore some of the implications of such extension results

global existence and uniform stabilization of a generalized dissipative klein gordon equation type with boundary damping in this paper we prove the existence uniqueness and uniform stability of strong and weak solutions of the nonlinear generalized klein gordon equation 1 1 1 see sec i in bounded domains with nonlinear damped boundary conditions given by 1 1 3 see sec i with some restrictions on function f u h u g ut and b x we prove the existence and uniqueness by means of nonlinear semigroup method and obtain the uniform stabilization by using the multiplier technique

stabilization of wave and plate like equations with nonlinear dissipation on the boundary abstract in this paper we consider second order in time equations of petrovsky type wave and plate like with nonlinear dissipative boundary conditions under certain geometric conditions imposed on the domain the results on asymptotic behavior of the solutions are established

a nonreflecting boundary condition for discrete acoustic and elastic wave equations one of the nagging problems which arises in application of discrete solution methods for wave propagation calculations is the presence of reflections or wraparound from the boundaries of the numerical mesh these undesired events eventually override the actual seismic signals which propagate in the modeled region the solution to avoiding boundary effects used to be to enlarge the numerical mesh thus delaying the side reflections and wraparound longer than the range of times involved in the modeling obviously this solution considerably increases the expense of computation more recently nonreflecting boundary conditions were introduced for the finite difference method clayton and enquist 1977 reynolds 1978 these boundary conditions are based on replacing the wave equation in the boundary region by one way wave equations which do not permit energy to propagate from the boundaries into the numerical mesh this approach has been relatively successful except that its effectiveness degrades for event

output feedback stabilization of an unstable wave equation we consider the problem of stabilization of a one dimensional wave equation that contains instability at its free end and control on the opposite end in contrast to classical collocated boundary damper feedbacks for the neutrally stable wave equations with one end satisfying a homogeneous boundary condition the controllers and the associated observers designed in the paper are more complex due to the open loop instability of the plant the controller and observer gains are designed using the method of backstepping which results in explicit formulae for the gain functions we prove exponential stability and the existence and uniqueness of classical solutions for the closed loop system we also derive the explicit compensators in frequency domain the results are illustrated with simulations

exact controllability of the euler bernoulli equation with boundary controls for displacement and moment abstract we consider the euler bernoulli problem 1 1 in the solution w t with boundary controls g1 and g2 acting in the dirichlet traces for w and w respectively we show two main exact controllability results both in the spaces of maximal regularity of the solution at t t see i lasiecka and r triggiani regularity theory for a class of euler bernoulli equations a cosine operator approach boll unione mat ital 7 3 b 1989 and both without geometrical conditions on the open bounded domain except for smoothness of its boundary one with g1 l2 0 t l2 and g2 h1 0 t l2 for any t 0 arbitrarily short and one with g1 h01 0 t l2 and g2 l2 0 t l2 for all t 0 sufficiently large an interpolation result between these two cases is also presented a direct approach is given based on two main steps first by means of an operator model i lasiecka and r triggiani regularity theory for a class of euler bernoulli equations a cosine operator approach boll unione mat ital 7 3 b 1989 for problem 1 1 and a functional analytic approach the question of exact controllability is shown to be equivalent to an a priori inequality for the corresponding homogeneous problem next this a priori inequality is proved to hold true by means of multiplier techniques these are inspired by recent progress on the maximal regularity exact controllability and uniform stabilization questions for second order hyperbolic equations

on existence and asymptotic stability of solutions of the degenerate wave equation with nonlinear boundary conditions abstract we study the global existence of solutions of the nonlinear degenerate wave equation 0 x y y 0 in 0 y 0 on 1 0 y y f y g y 0 on 0 0 y x 0 y 0 y x 0 y 1 x in where y denotes the derivative of y with respect to parameter t f s c0 s s and g is a nondecreasing c1 function such that k1 s 2 g s s k2 s 2 for some k1 k2 0 with 0 0 if n 1 2 the existence of solutions is proved by means of the faedo galerkin method furthermore when 0 the uniform decay is obtained by making use of the perturbed energy method

error analysis for absorbing boundary conditions an estimate is derived for the error committed by the introduction of artificial boundaries and corresponding artificial boundary conditions when solving wave equations on unbounded domains the estimate has two terms one is proportional to the largest reflection coefficient for the artificial boundary condition the maximum taken only on those rays which appear in the computation the second term is proportional to 1 k wherek is a measure of the average frequency present in the solution

stabilization of a transmission wave plate equation abstract we consider a stabilization problem for a model arising in the control of noise coupling the damped wave equation with a damped kirchhoff plate equation we prove an exponential stability result under some geometric condition our method is based on an identity with multipliers that allows to show an appropriate energy estimate

new upper bounds on the size of codes correcting asymmetric errors corresp new upper bounds on the size of codes correcting asymmetric errors are derived by sharpening some of the constraints in the integer programming problem of delsarte and piret it is shown that their code for length 9 and asymmetric distance 2 is optimal

shape sensitivity for the laplace beltrami operator with singularities this paper considers shape sensitivity analysis for the laplace beltrami operator formulated on a two dimensional manifold with a fracture we characterize the shape gradient of a functional as a bounded measure on the manifold and decompose it into a distributed gradient supported on the manifold plus a singular part that we derive as the limit of a jump through the crack and dirac measures at the crack extremities the important point is that we introduce a technique that is not dimension dependent and makes no use of classical arguments such as the maximum principle or continuation uniqueness the technique makes use of a family of envelopes surrounding the fracture which enable us to relax certain terms and to overcome the lack of regularity resulting from the presence of the fracture we use the min max differentiation in order to avoid taking the derivative of the state equation and to manage the crack s singularities therefore we write the functional in a min max formulation on a space which takes into account the hidden boundary regularity established by the tangential extractor method

stabilization of euler bernoulli plate equation with variable coefficients by nonlinear boundary feedback abstract the aim of this paper is to investigate the uniform stabilization of euler bernoulli plate equation with variable coefficients in the principle part subject to nonlinear boundary feedback laws the exponential or rational energy decay rate is obtained by the multiplier method and the riemannian geometry method

a subcell remapping method on staggered polygonal grids for arbitrary lagrangian eulerian methods we describe a new remapping algorithm for use in arbitrary lagrangian eulerian ale simulations the new features of this remapper are designed to complement a staggered mesh lagrangian phase in which the cells may be general polygons in two dimensions and which uses subcell discretizations to control unphysical mesh distortion and hourglassing our new remapping algorithm consists of three stages a gathering stage in which we interpolate momentum internal energy and kinetic energy to the subcells in a conservative way a subcell remapping stage in which we conservatively remap mass momentum internal and kinetic energy from the subcells of the lagrangian mesh to the subcells of the new rezoned mesh a scattering stage in which we conservatively recover the primary variables subcell density nodal velocity and cell centered specific internal energy on the new rezoned mesh we prove that our new remapping algorithm is conservative reversible and satisfies the debar consistency condition we also demonstrate computationally that our new remapping method is robust and accurate for a series of test problems in one and two dimensions

identification of a free boundary in norton hoff flows with thermal effects this work deals with a free boundary identification problem in a steady viscoplastic flow we provide a novel identification model based on a non linear optimization the fluid motion is governed by the incompressible norton hoff model coupled with the heat equation the viscosity of the fluid is modeled by the non linear arrhenius law our point of view is to treat the problem as a shape sensitivity of a cost functional formulated on the free boundary and governed by the normal component of the velocity of the flow we analyze the mathematical statement of the forward problem the equations related to the free boundary are simplified various properties of this optimization are proved since the state of norton hoff model is not regular enough we introduce a parameter penalization the shape gradient of the considered cost functional is given in the strong sense up to the parameter of penalization we supply the expression of the shape gradient in a weak sense

a note on the boundary stabilization of the wave equation we study the energy decay rates of the wave equation in a domain where boundary damping is present we generalize the geometrical conditions obtained earlier in j math purer appl 58 1979 pp 249 273 by using some more general multipliers of strauss comm pure appl math 28 1975 pp 265 278 the interaction between distributed damping and boundary damping is discussed a regulator problem is also formally discussed by the synthesis method

control of singular problem via differentiation of a min max abstract for a smooth domain in r n with boundary 0 1 we are concerned with the wave equation y y s in q t 0 t with t at source term satisfying s s l 1 0 t l 2 a dirichlet condition is imposed on 0 and we consider an absorbing condition y n uy 0 in 0 t gl 1 where u is the control parameter we introduce the cost function j u 1 2 t 0 1 uy 2 d d t and using the min max formulation of j we by pasas the sensitivity analysis of u y and obtain the gradient of j with a usual adjoint problem we first present an abstract frame for this kind of problems using the differentiability results of a min max 1 2 which we very shortly deduce here we show that the well posedness of the adjoint equation implies differentiability of the cost function governed by a linear well posed problem

a two dimensional unstructured cell centered multi material ale scheme using vof interface reconstruction we present a new cell centered multi material arbitrary lagrangian eulerian ale scheme to solve the compressible gas dynamics equations on two dimensional unstructured grid our ale method is of the explicit time marching lagrange plus remap type namely it involves the following three phases a lagrangian phase wherein the flow is advanced using a cell centered scheme a rezone phase in which the nodes of the computational grid are moved to more optimal positions a cell centered remap phase which consists of interpolating conservatively the lagrangian solution onto the rezoned grid the multi material modeling utilizes either concentration equations for miscible fluids or the volume of fluid vof capability with interface reconstruction for immiscible fluids the main original feature of this ale scheme lies in the introduction of a new mesh relaxation procedure which keeps the rezoned grid as close as possible to the lagrangian one in this formalism the rezoned grid is defined as a convex combination between the lagrangian grid and the grid resulting from condition number smoothing this convex combination is constructed through the use of a scalar parameter which is a scalar function of the invariants of the cauchy green tensor over the lagrangian phase regarding the cell centered remap phase we employ two classical methods based on a partition of the rezoned cell in terms of its overlap with the lagrangian cells the first one is a simplified swept face based method whereas the second one is a cell intersection based method our multi material ale methodology is assessed through several demanding two dimensional tests the corresponding numerical results provide a clear evidence of the robustness and the accuracy of this new scheme

boundary observability controllability and stabilization of linear elastodynamic systems in 1988 lions obtained observability and exact controllability results for linear homogeneous isotropic elastodynamic systems siam rev 30 1988 pp 1 68 applying some new identities we extend his theorems to nonisotropic systems in 1991 lagnese obtained uniform stabilizability results for two dimensional linear homogeneous isotropic systems by applying a somewhat artificial feedback nonlinear anal 16 1991 pp 35 54 then he asked whether analogous results hold for a natural and physically implementable boundary feedback using some new identities and applying a method introduced in 1987 by zuazua and the second author j math pures appl 69 1990 pp 33 54 we give an affirmative answer to this question in all dimensions and also for nonisotropic systems moreover we obtain good decay estimates finally applying a recent general method of uniform stabilization we construct boundary feedbacks leading to arbitrarily large energy decay rates

regularity of higher energies of wave equation with nonlinear localized damping and a nonlinear source abstract wave equation driven by a nonlinear dissipative source and subjected to a nonlinear damping that is localized on a small region near the boundary is considered while finite energy h 1 l 2 solutions to this problem are bounded uniformly for all times t 0 this property generally fails for higher energy norms h 2 h 1 this is due to a generation of higher energy by the source and the ultimate loss of dissipativity however the presence of the damping may turn things around by counteracting the sources also at the higher energy levels the benefits of this counteraction depend on the nonlinear characteristics of dissipation any deviation from linearity be it origin or infinity causes degradation of the damping hence of decay rates of finite energy this in turn is shown to have an adverse effect on the stability of higher energies the main aim of this paper is to provide a quantitative analysis of the interaction between nonlinearity of the damping and nonlinearity of the source we show that under some correlation between growth rates of the damping and the source the norms of topological order above the finite energy level remain globally bounded for all times

on exponential stability of a semilinear wave equation with variable coefficients under the nonlinear boundary feedback abstract the uniform stabilization of an originally regarded nondissipative system described by a semilinear wave equation with variable coefficients under the nonlinear boundary feedback is considered the existence of both weak and strong solutions to the system is proven by the galerkin method the exponential stability of the system is obtained by introducing an equivalent energy function and using the energy multiplier method on the riemannian manifold this equivalent energy function shows particularly that the system is essentially a dissipative system this result not only generalizes the result from constant coefficients to variable coefficients for these kinds of semilinear wave equations but also simplifies significantly the proof for constant coefficients case considered in a guesmia a new approach of stabilization of nondissipative distributed systems siam j control optim 42 2003 24 52 where the system is claimed to be nondissipative

bounds and constructions for binary codes of length less than 24 and asymmetric distance less than 6 upper bounds to the maximum number of codewords in a binary code of length n and asymmetric distance delta are derived for some values of n and delta a method is given in which a code of length n m and asymmetric distance at least t 1 is constructed by expurgating and puncturing a code of length n and hamming distance at least 2t 1 novel asymmetric error correcting codes are constructed by applying this method to some celebrated symmetric error correcting codes a table is presented on the size of optimal asymmetric error correcting codes of length less than 24 and asymmetric distance less than 6

decay of solutions of wave equations in a bounded region with boundary dissipation abstract an energy decay rate is obtained for solutions of wave type equations in a bounded region in rn whose boundary consists partly of a nontrapping reflecting surface and partly of an energy absorbing surface

global existence for the wave equation with nonlinear boundary damping and source terms abstract the paper deals with local and global existence for the solutions of the wave equation in bounded domains with nonlinear boundary damping and source terms the typical problem studied is u tt u 0 in 0 u 0 on 0 0 u u t m 2 u t u p 2 u on 0 1 u 0 x u 0 x u t 0 x u 1 x on where r n n 1 is a regular and bounded domain 0 1 m 1 2 p r where r 2 n 1 n 2 when n 3 r when n 1 2 and the initial data are in the energy space we prove local existence of the solutions in the energy space when m r r 1 p or n 1 2 and global existence when p m or the initial data are inside the potential well associated to the stationary problem

high order multi material ale hydrodynamics we present a new approach for multi material arbitrary lagrangian eulerian ale hydrodynamics simulations based on high order finite elements posed on high order curvilinear meshes the method builds on and extends our previous work in the lagrangian v a dobrev t v kolev and r n rieben siam j sci comput 34 2012 pp b606 b641 and remap r w anderson et al internat j numer methods fluids 77 2015 pp 249 273 phases of ale and depends critically on a functional perspective that enables subzonal physics and material modeling v a dobrev et al internat j numer methods fluids 82 2016 pp 689 706 curvilinear mesh relaxation is based on node movement which is determined through the solution of an elliptic equation the remap phase is posed in terms of advecting state variables between two meshes over a fictitious time interval the resulting advection equation is solved by a discontinuous galerkin dg formulation combined with a customized flux corrected transpor

second order parabolic equations in banach spaces with dynamic boundary conditions in this paper we exhibit a unified treatment of the mixed initial boundary value problem for second order in time parabolic linear differential equations in banach spaces whose boundary conditions are of a dynamical nature results regarding existence uniqueness continuous dependence on initial data and regularity of classical and strict solutions are established moreover several examples are given as samples for possible applications

energy decay rates for the semilinear wave equation with nonlinear localized damping and source terms abstract in this paper we develop an intrinsic approach to derivation of energy decay rates for the semilinear wave equation with localized interior nonlinear monotone damping g u t and a source term f u the proposed approach allows to consider in an unified way much more general classes of hyperbolic problems than addressed before in the literature these generalizations refer to both geometric and topological aspects of the problem the method leads to optimal decay rates for solutions of semilinear hyperbolic equations driven by a source of critical exponent and subjected to a nonlinear damping localized in a small region adjacent to a portion of the boundary the distinct features of the model include i neumann boundary conditions are assumed and ii no growth conditions are imposed on the damping g s it is well known that neumann boundary does not satisfy lopatinski condition and therefore the analysis of propagation of energy in the absence of the damping on the neumann part of the boundary requires special geometric considerations in addition the sole conditions assumed on g s are monotonicity continuity and g 0 0 in particular no differentiability and no growth conditions are imposed on the damping both at the origin and at the infinity the asymptotic decay rates for the energy function are obtained from an intrinsic algorithm driven by solutions of simple ode several examples illustrate the theory by exhibiting various decay rates exponential algebraic rational logarithmic etc for the energy functional an important corollary of our energy decay theorem is a stability result which shows that under certain conditions when dissipation is sublinear at infinity the solution of the system remains uniformly bounded for all time in the norms above the finite energy level even in the presence of a nonlinear source term

an identity in combinatorial extremal theory abstract our main discovery is the following identity for every family a 2 of non empty subsets of 1 2 n x w a x x n x 1 where w a x x a a a it can be viewed as a sharpening of the famous lym inequality we present also generalizations to other posets the total impact for combinatorics remains to be explored the identity seems to be particularly useful for uniqueness proofs in sperner theory we also discuss a geometric consequence

the mixed problem in l p for some two dimensional lipschitz domains we consider the mixed problem left begin array ll delta u 0 quad rm in omega frac partial u partial nu f n quad rm on rm n u f d quad rm on d end array right in a class of lipschitz graph domains in two dimensions with lipschitz constant at most 1 we suppose the dirichlet data fd has one derivative in lp d of the boundary and the neumann data fn is in lp n we find a p0 1 so that for p in an interval 1 p0 we may find a unique solution to the mixed problem and the gradient of the solution lies in lp

variational method for untangling and optimization of spatial meshes a variational method that can provably construct 3d quasi isometric mappings between domains of a complex shape is introduced a local maximum principle for polyconvex mesh element distortion measures is formulated it allows us to control the invertibility and distortion bounds for non simplicial elements in the minimization process a simple and efficient technique for construction of boundary orthogonal meshes suggested in garanzha 2000 is applied to the construction of hexahedral meshes and thick prismatic mesh layers around complex shapes the mesh untangling technique which is a generalization of the penalty method suggested in garanzha and kaporin 1999 is verified on a wide set of challenging test problems another untangling technique based on theoretical ideas from ivanenko 1997 is implemented and tested it provably constructs admissible meshes using a finite number of minimization steps a minimization technique for the mesh distortion functional is described the approach is based on the global gradient search technique with preconditioning and domain decomposition for local mesh optimization and untangling application areas for explicit and implicit minimization methods are evaluated

second order systems with acceleration measurements accelerometers are often used to measure the output of second order systems such as structural vibrations conditions under which these systems are well posed are obtained we also establish conditions under which these systems have minimum phase transfer functions

a single asymmetric error correcting code with 2 sup 13 codewords of dimension 17 a new single asymmetric error correcting code is proposed this code is constructed using a product of two codes of smaller dimensions the proposed code is of dimension 17 and of size 8192 i e with 2 sup 13 codewords the best known code of dimension 17 has size 7968 and capable of handling 12 information bits only the only other three known cases of single asymmetric codes accommodating one more extra information bit than the symmetric case are for code dimensions 2 4 and 16

new lower bounds for binary codes of asymmetric distance two lower bounds for asymmetric single error correcting codes are derived the codes are constructed by puncturing constant weight codes and by using a random coding argument

unknown input observer design and output feedback stabilization for multi dimensional wave equation with boundary control matched uncertainty abstract in this paper we consider boundary output feedback stabilization for a multi dimensional wave equation with boundary control matched unknown nonlinear internal uncertainty and external disturbance a new unknown input type extended state observer is proposed to recover both state and total disturbance which consists of internal uncertainty and external disturbance a key feature of the proposed observer in this paper is that we do not use the high gain to estimate the disturbance by the active disturbance rejection control adrc strategy the total disturbance is compensated canceled in the feedback loop which together with a collocated stabilizing controller without uncertainty leads to an output feedback stabilizing feedback control it is shown that the resulting closed loop system is well posed and asymptotically stable under weak assumption on internal uncertainty and external disturbance the numerical experiments are carried out to show the effectiveness of the proposed scheme

dirichlet feedback control for the stabilization of the wave equation a numerical approach abstract in j differential equations 66 1987 340 a uniform stabilization method of the wave equation by boundary control a la dirichlet has been discussed in this article we investigate the numerical implementation of the above stabilization process by a numerical scheme which mimics the energy decay properties of its continuous counterpart the practical implementation of that scheme leads to a biharmonic problem of a new type which is solved by a method directly inspired by some related work of glowinski and pironneau on the solution of the dirichlet problem for the biharmonic operator siam rev 21 2 1979 167 numerical experiments show that the decay properties of the energy are well preserved by our numerical methodology

complete second order differential equations in banach spaces with dynamic boundary conditions abstract in this paper we deal with the mixed initial boundary value problem for complete second order in time linear differential equations in banach spaces in which time derivatives occur in the boundary conditions general wellposedness theorems are obtained for the first time which are used to solve the corresponding inhomogeneous problems examples of applications to initial boundary value problems for partial differential equations are also presented

new single asymmetric error correcting codes new single asymmetric error correcting codes are proposed these codes are better than existing codes when the code length n is greater than 10 except for n 12 and n 15 in many cases one can construct a code c containing at least 2 sup n n codewords it is known that a code with c spl ges 2 sup n n 1 can be easily obtained it should be noted that the proposed codes for n 12 and n 15 are also the best known codes that can be explicitly constructed since the best of the existing codes for these values of n are based on combinatorial arguments useful partitions of binary vectors are also presented

dynamical boundary control of two dimensional wave equations vibrating membrane on general domain dynamical boundary control of a vibrating membrane with edge mass and of general shape is mathematically formulated as an abstract evolutionary system the approximate controllability and the strong stabilization by linear boundary damping feedback are established by an approach based on lasalle s invariance principle the mathematical model and the reduced system can be used to investigate some optimization problems

a new table of constant weight codes a table of binary constant weight codes of length nl28 is presented explicit constructions are given for most of the 600 codes in the table the majority of these codes are new the known techniques for constructing constant weight codes are surveyed and a table of unrestricted binary codes of length nl28 is given

stabilization of cell centered compressible lagrangian methods using subzonal entropy this work deals with the stabilization of early stages of lagrangian calculations of compressible gas dynamics in the context of cell centered discretization we describe a totally conservative algorithm based on an entropy analysis of the distortion of a lagrangian mesh it prevents the tangling of the mesh while remaining consistent and conservative in mass momentum and total energy the method described can be applied to any cell centered lagrangian scheme in this article we detail the extension to the cell centered glace scheme published in carre et al 2009 g carre s del pino b despres e labourasse a cell centered lagrangian hydrodynamics scheme on general unstructured meshes in arbitrary dimension j comput phys 228 2009 5160 5183 numerical tests are proposed to assess the accuracy and robustness