stabilization for wave equation of variable coefficients with balakrishnan taylor damping and source term abstract in this paper we consider the wave equation of variable coefficients with balakrishnan taylor damping time varying delay and source term by establishing some lyapunov functionals which are equivalent to the energy of the system and using the potential well method to deal with the source term we prove a general stability result

on a system of klein gordon type equations with acoustic boundary conditions we prove the existence uniqueness and uniform stabilization of global solutions for a generalized system of klein gordon type equations with acoustic boundary conditions on a portion of the boundary and the dirichlet boundary condition on the rest

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

some nonlinear wave equations with acoustic boundary conditions abstract we prove the existence and uniqueness of global solutions to the mixed problem for the carrier equation u tt m u 2 dx u u t u t 0 with acoustic boundary conditions

energy decay of a variable coefficient wave equation with memory type acoustic boundary conditions abstract we study the energy decay for a variable coefficient wave equation with memory type acoustic boundary conditions boundary memory is described by an integral term applying the riemannian geometry method we obtain the uniform energy decay under some conditions on the memory function and the coefficient matrix

existence of a solution of the wave equation with nonlinear damping and source terms abstract we study the nonlinear wave equation involving the nonlinear damping term u t u t m 1 and a source term of type u u p 1 for 1 p m we prove a global existence theorem with large initial data for 1 m p a blow up result is established for sufficiently large initial data

the hierarchical basis multigrid method we derive and analyze the hierarchical basis multigrid method for solving discretizations of self adjoint elliptic boundary value problems using piecewise linear triangular finite elements the method is analyzed as a block symmetric gau seidel iteration with inner iterations but it is strongly related to 2 level methods to the standard multigridv cycle and to earlier jacobi like hierarchical basis methods the method is very robust and has a nearly optimal convergence rate and work estimate it is especially well suited to difficult problems with rough solutions discretized using highly nonuniform adaptively refined meshes

uniform stabilization of the damped cauchy ventcel problem with variable coefficients and dynamic boundary conditions in this paper the uniform stabilization of the cauchy ventcel problem with variable coefficients is considered and the uniform energy decay rate for the problem is established by riemannian geometry methods

approximation theorems for the propagators of higher order abstract cauchy problems in this paper we present two quite general approximation theorems for the propagators of higher order in time abstract cauchy problems which extend largely the classical trotter kato type approximation theorems for strongly continuous operator semigroups and cosine operator functions then we apply the approximation theorems to deal with the second order dynamical boundary value problems

robustness of multi grid applied to anisotropic equations on convex domains and on domains with re entrant corners we analyse multi grid applied to anisotropic equations within the framework of smoothing and approximation properties developed by hack busch for a model anisotropic equation on a square we give an up till now missing proof of an estimate concerning the approximation property which is essential to show robustness furthermore we show a corresponding estimate for a model anisotropic equation on an l shaped domain the existing estimates for the smoothing property are not suitable to prove robustness for either 2 cyclic gauss seidel smoothers or for less regular problems such as our second model equation for both cases we give sharper estimates by combination of our results concerning smoothing and approximation properties robustness of w cycle multi grid applied to both our model equations will follow for a number of smoothers

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

black box multigrid one major problem with the multigrid method has been that each new grid configuration has required a major programming effort to develop a code that specifically handles that grid configuration such a penalty is not required for methods like sor iccg etc in these methods one need only specify the matrix problem no matter what the grid configuration in this paper we investigate such a situation for the multigrid method the end result is code boxmg in which one need only specify the logically rectangular positive definite matrix problem boxmg does everything else necessary to set up the auxilliary coarser problems to achieve a multigrid solution

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

robust parallel smoothing for multigrid via sparse approximate inverses sparse approximate inverses are considered as smoothers for multigrid they are based on the spai algorithm m j grote and t huckle siam j sci comput 18 1997 pp 838 853 which constructs a sparse approximate inverse m of a matrix a by minimizing i ma in the frobenius norm this yields a new hierarchy of smoothers spai 0 spai 1 spai varepsilon advantages of spai smoothers over classical smoothers are inherent parallelism possible local adaptivity and improved robustness the simplest smoother spai 0 is based on a diagonal matrix m it is shown to satisfy the smoothing property for symmetric positive definite problems numerical experiments show that spai 0 smoothing is usually preferable to damped jacobi smoothing for the spai 1 smoother the sparsity pattern of m is that of a its performance is typically comparable to that of gauss seidel smoothing however both the computation and the application of the smoother remain inherently parallel in more difficult situations where the simpler spai 0 and spai 1 smoothers are not adequate the spai varepsilon smoother provides a natural procedure for improvement where needed numerical examples illustrate the usefulness of spai smoothing

asymptotic stability of the wave equation on compact surfaces and locally distributed damping a sharp result this paper is concerned with the study of the wave equation on compact surfaces and locally distributed damping described by u tt m u x g u t 0 on m 0 where m c r 3 is a smooth oriented embedded compact surface without boundary denoting by g the riemannian metric induced on m by r 3 we prove that for each 0 there exist an open subset v c m and a smooth function f m r such that meas v meas m e hessf g on v and inf f x 0 x v in addition we prove that if x a o 0 on an open subset m c m which contains m v and if g is a monotonic increasing function such that k s g s k s for all s 1 then uniform and optimal decay rates of the energy hold

regularity theory of hyperbolic equations with non homogeneous neumann boundary conditions ii general boundary data abstract this paper studies the regularity of solutions of general mixed second order time dependent hyperbolic problems of neumann type in a previous paper i lasiecka and r triggiani ann mat pura appl iv clvii 1990 285 367 using pseudo differential calculus we have provided sharp regularity results of the solutions and their traces when the non homogeneous data are in l 2 now we complement this study by providing a regularity when the non homogeneous data are more regular than as well as less regular than l 2 in contrast with our previous paper a functional analytic approach based on the l 2 results of our previous paper is used throughout

on the wave equation with semilinear porous acoustic boundary conditions the goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary interior sources and a nonlinear boundary interior damping first applying the nonlinear semigroup theory we show the existence and uniqueness of local in time solutions the main difficulty in proving the local existence result is that the neumann boundary conditions experience loss of regularity due to boundary sources using an approximation method involving truncated sources and adapting the ideas in lasiecka and tataru 1993 28 we show that the existence of solutions can still be obtained second we prove that under some restrictions on the source terms then the local solution can be extended to be global in time in addition it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ode and depends on the behavior of the damping terms in several situations the obtained ode can be easily solved and the decay rates can be given explicitly third we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping then the solution ceases to exists and blows up in finite time moreover in either the absence of the interior source or the boundary source then we prove that the solution is unbounded and grows as an exponential function

stabilization of the variable coefficient structural acoustic model with curved middle surface and delay effects in the structural component abstract this paper is concerned with the uniform energy decay rates of a structural acoustic model which describes the interactions between the acoustic medium and the elastic structural in an acoustic chamber where one wall is flexible and curved the coupled system considered consists of a variable coefficient wave equation and a variable coefficient plate equation defined on the riemannian manifold with the coupling on the interface between the acoustic medium and the flexible wall both the components of the dynamics are subject to nonlinear boundary damping furthermore a nonlinear delay term acting in the boundary feedbacks of the structure component is considered the riemannian geometry method is applied to derive the energy estimates of the nonlinear coupled system with variable coefficients the uniform energy decay rates of the nonlinear variable coefficient structural acoustic system with delay effects on the riemannian manifold are quantified by a solution to a constructed nonlinear ode

ilum a multi elimination ilu preconditioner for general sparse matrices standard preconditioning techniques based on incomplete lu ilu factorizations offer a limited degree of parallelism in general a few of the alternatives advocated so far consist of either using some form of polynomial preconditioning or applying the usual ilu factorization to a matrix obtained from a multicolor ordering in this paper we present an incomplete factorization technique based on independent set orderings and multicoloring we note that in order to improve robustness it is necessary to allow the preconditioner to have an arbitrarily high accuracy as is done with ilus based on threshold techniques the ilum factorization described in this paper is in this category it can be viewed as a multifrontal version of a gaussian elimination procedure with threshold dropping which has a high degree of potential parallelism the emphasis is on methods that deal specifically with general unstructured sparse matrices such as those arising from finite element methods on unstructured meshes

local hadamard well posedness for nonlinear wave equations with supercritical sources and damping abstract we consider the wave equation with supercritical interior and boundary sources and damping terms the main result of the paper is local hadamard well posedness of finite energy weak solutions the results obtained 1 extend the existence results previously obtained in the literature by allowing more singular sources 2 show that the corresponding solutions satisfy hadamard well posedness conditions during the time of existence this result provides a positive answer to an open question in the area and it allows for the construction of a strongly continuous semigroup representing the dynamics governed by the wave equation with supercritical sources and damping

on nonlinear wave equations of carrier type abstract this paper is concerned with the initial boundary value problem of the n dimensional carrier equation with an internal damping this damping is a fractional power of the velocity of the points of the material the faedo galerkin method tartar approach and compactness arguments provide the global existence of solutions of the above problem with restriction on the size of the initial data the decay of solutions is obtained by the perturbation method

optimal nested row column designs with specified components we consider nested row column designs where each of the row and column component designs is specified for the case that each of the component designs has second order balance we define such a nested row column design to be special if it is generally balanced with the smallest possible number of canonical treatment contrasts having the lower canonical efficiency factor in both components we show that if any special row column design exists then it is a optimal over all nested row column designs with the given components

existence and decay of solutions for a viscoelastic wave equation with acoustic boundary conditions abstract in this paper we consider a multi dimensional damped semilinear viscoelastic wave equation with variable coefficient and acoustic boundary conditions first we prove a local existence theorem by using the faedo galerkin approximations combined with a contraction mapping theorem second we show that under suitable conditions on the initial data and the relaxation function the solution exists globally in time and we prove the uniform decay rate of the energy

on the observability inequalities for exact controllability of wave equations with variable coefficients this paper deals with boundary exact controllability for the dynamics governed by the wave equation with nonconstant coefficients in the principal part subject to dirichlet or neumann boundary controls the observability inequalities are established by the riemannian geometry method under some geometric condition for the dirichlet problem and for the neumann problem respectively next a number of nontrivial examples are presented to verify the observability inequality in particular a counterexample is given without boundary exact controllability where the control is exerted on the whole boundary

stabilization of the transmission wave plate equation with variable coefficients abstract we consider the stabilization of the transmission wave plate equation with variable coefficients and a general transmission boundary by virtue of the riemannian geometric approach we obtain some stability results for nonlinear feedbacks acting on the regions under suitable geometric conditions

decay estimates for some semilinear damped hyperbolic problems let be a bounded open domain in rn g r r a non decreasing continuous function such that g 0 0 and h e lloc1 r l2 under suitable assumptions on g and h the rate of decay of the difference of two solutions is studied for some abstract evolution equations of the general form u lu g u h t x as t the results obtained by use of differential inequalities can be applied to the case of the semilinear wave equation u u delta u g text u t text h text in r times omega text u text 0 on r times partial omega in r u 0 onr for instance if g s c left s right p 1 s d left s right q 1 s with c d 0 and 1 p q n 2 q n 2 then if h in l infty r l 2 omega all solutions are bounded in the energy space for t 0 and if u v are two such solutions the energy norm of u t v t decays like t 1 p 1 as t

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

decay rate estimates for wave equations of memory type with acoustic boundary conditions abstract a wave equation of memory type u u 0 t g t s u s d s 0 with acoustic boundary conditions is considered this work is devoted to investigating the influence of the kernel function g and proving general rates of decay of solutions when g does not necessarily decay exponentially

parallel accelerated cyclic reduction preconditioner for three dimensional elliptic pdes with variable coefficients abstract we present a robust and scalable preconditioner for the solution of large scale linear systems that arise from the discretization of elliptic pdes amenable to rank compression the preconditioner is based on hierarchical low rank approximations and the cyclic reduction method the setup and application phases of the preconditioner achieve log linear complexity in memory footprint and number of operations and numerical experiments exhibit good weak and strong scalability at large processor counts in a distributed memory environment numerical experiments with linear systems that feature symmetry and nonsymmetry definiteness and indefiniteness constant and variable coefficients demonstrate the preconditioner applicability and robustness furthermore it is possible to control the number of iterations via the accuracy threshold of the hierarchical matrix approximations and their arithmetic operations and the tuning of the admissibility condition parameter together these parameters allow for optimization of the memory requirements and performance of the preconditioner

well posedness and regularity of naghdi s shell equation under boundary control and observation abstract a system of naghdi s shell equation with dirichlet boundary control and collocated observation is considered results on the associated nonhomogeneous boundary value problem are presented based on these results it is shown that the system is well posed in the sense of d salamon and regular in the sense of g weiss the expression of the corresponding feedthrough operator is explicitly found by means of riemannian geometric method and partial fourier transform these properties make this partial differential control system parallel in many ways finite dimensional ones in the general framework of well posed and regular infinite dimensional systems

optimal g closure bounds via stability under lamination optimal bounds for a two dimensional g closure problem are proved they are obtained by combining together bounds derived using fine properties of quasiconformal mappings and a stability property of the g closure which is known as stability under lamination

on a mixed problem with a nonlinear acoustic boundary condition for a non locally reacting boundaries abstract we discuss global solvability to the mixed problem for a nonlinear wave equation in domains with non locally reacting boundaries and nonlinear acoustic boundary condition we prove the existence and uniqueness of solution additionally using the method of nakao we demonstrate the decay of the associated energy stability

global smooth solutions for the quasilinear wave equation with boundary dissipation abstract we consider the existence of global solutions of the quasilinear wave equation with a boundary dissipation structure of an input output in high dimensions when initial data and boundary inputs are near a given equilibrium of the system our main tool is the geometrical analysis the main interest is to study the effect of the boundary dissipation structure on solutions of the quasilinear system we show that the existence of global solutions depends not only on this dissipation structure but also on a riemannian metric given by the coefficients and the equilibrium of the system some geometrical conditions on this riemannian metric are presented to guarantee the existence of global solutions in particular we prove that the norm of the state of the system decays exponentially if the input stops after a finite time which implies the exponential stabilization of the system by boundary feedback

inverse observability estimates for second order hyperbolic equations with variable coefficients abstract we consider a general second order hyperbolic equation defined on an open bounded domain r n with variable coefficients in both the elliptic principal part and in the first order terms as well at first no boundary conditions b c are imposed our main result theorem 3 5 is a reconstruction or inverse estimate for solutions w under checkable conditions on the coefficients of the principal part the h1 l2 energy at time t t or at time t 0 is dominated by the l2 norms of the boundary traces w a and wt modulo an interior lower order term once homogeneous b c are imposed our results yield under a uniqueness theorem needed to absorb the lower order term continuous observability estimates for both the dirichlet and neumann case with an explicit sharp observability time hence by duality exact controllability results moreover no artificial geometrical conditions are imposed on the controlled part of the boundary in the neumann case in contrast with existing literature the first step of our method employs a riemann geometry approach to reduce the original variable coefficient principal part problem in r n to a problem on an appropriate riemann manifold determined by the coefficients of the principal part where the principal part is the laplacian in our second step we employ explicit carleman estimates at the differential level to take care of the variable first order energy level terms in our third step we employ micro local analysis yielding a sharp trace estimate to remove artificial geometrical conditions on the controlled part of the boundary in the neumann case

wave equation with porous nonlinear acoustic boundary conditions generates a well posed dynamical system we consider a structural acoustic wave equation with nonlinear acoustic boundary conditions this is a coupled system of second and first order in time partial differential equations with boundary conditions on the interface we prove wellposedness in the hadamard sense for strong and weak solutions the main tool used in the proof is the theory of nonlinear semigroups we present the system of partial differential equations as a suitable cauchy problem dw dt aw though the operator a is not maximally dissipative we are able to show that it is a translate of a maximally dissipative operator the obtained semigroup solution is shown to satisfy a suitable variational equality thus giving weak solutions to the system of pdes the results obtained i dispel the notion that the model does not generate semigroup solutions ii provide treatment of nonlinear models and iii provide existence of a correct state space which is invariant under the flow thus showing that physical model under consideration is a dynamical system the latter is obtained by eliminating compatibility conditions which have been assumed in previous work on the linear case

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

global smooth solutions of the quasi linear wave equation with internal velocity feedback we study the existence of global smooth solutions for the quasi linear wave equation by an internal local damping when initial data are close to a given equilibrium our interest is in studying the structure of the damping region which guarantees the existence of global solutions our results show that the structure of the damping region depends on the geometric properties of a riemannian metric based on the coefficients and the equilibrium of the system some geometrical conditions are presented to obtain the damping region

the abstract cauchy problem for dissipative operators with respect to metric like functionals abstract this paper is devoted to a characterization of semigroups of lipschitz operators on a closed subset d of a banach space x and the abstract cauchy problem for an operator a in x satisfying the following condition there exists a proper lower semicontinuous functional from x into 0 such that the effective domain of is d a and such that lim n a x n a x in x for any x d a and any sequence x n in d a satisfying two conditions lim n x n x in x and lim sup n x n x the main result asserts that a semigroup of lipschitz operators on d can be generated by an operator a satisfying the above mentioned condition a dissipative condition with respect to a metric like functional and a subtangential condition the kirchhoff equations with acoustic boundary conditions are solved by the method based on the abstract result with the construction of suitable liapunov functionals and the use of a metric like functional on a suitable set

general stability of a viscoelastic variable coefficients plate equation with time varying delay in localized nonlinear internal feedback abstract this paper is concerned with the decay properties of a memory type euler bernoulli plate equation with variable coefficients and time varying delay in localized nonlinear internal feedback by using piecewise multiplier method and riemannian geometric analysis we establish the explicit and general decay rates of system whose nonlinear internal feedbacks act on a suitable subregion

exact controllability stabilization and perturbations for distributed systems exact controllability is studied for distributed systems of hyperbolic type or for petrowsky systems like plate equations the control is a boundary control or a local distributed control exact controllability consists in trying to drive the system to rest in a given finite time the solution of the problems depends on the function spaces where the initial data are taken and also depends on the function space where the control can be chosen a systematic method named hum for hilbert uniqueness method is introduced as the terminology indicates it is based on uniqueness results classical or new and on hilbert spaces constructed in infinitely many ways by using uniqueness a number of applications are indicated having a general method for exact controllability implies having a general method for stabilization this leads to new and complicated nonlinear riccati s type pdes to be compared with direct methods when available in the last part of the paper we consider how all this behaves fo

an application of semigroups of locally lipschitz operators to carrier equations with acoustic boundary conditions abstract a generation theorem of semigroups of locally lipschitz operators on a subset of a real banach space is given and applied to the problem of the well posedness of the carrier equation u t t u 2 u u t p 1 u t 0 in 0 with acoustic boundary condition where p 2 and is a bounded domain in an arbitrary dimensional space

quasilinear hyperbolic 2 2 systems with a free damping boundary condition we consider a quasilinear system of equations for two functions u x t v x t and a boundary function s t

uniform energy decay of a variable coefficient wave equation with nonlinear acoustic boundary conditions abstract a variable coefficient wave equation with nonlinear damped acoustic boundary conditions is considered the riemannian geometry method is applied to deal with the variable coefficients under some checkable conditions on the coefficients the uniform decay of the energy is achieved without any geometrical conditions on the shape of the dissipative portion of the boundary

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

polynomial stability for wave equations with acoustic boundary conditions and boundary memory damping we study wave equations with acoustic boundary conditions where only one memory damping acts on the acoustic boundary under some conditions on the memory kernel polynomial energy decay rates are established by using higher order energy estimates among some other techniques

well posedness and optimal decay rates for the wave equation with nonlinear boundary damping source interaction we establish subject to some natural additional assumptions imposed on the relation between the source and the damping both well posedness and effective optimal decay rates for the solutions of a semilinear model of the wave equation the theory presented allows to consider both superlinear and sublinear behaviours of the dissipation in the presence of unstructured sources

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

the analysis of lattice square designs on donne une definition generale et on donne une approche unifiee a l analyse d une classe restreinte de tels plans

well posedness for a variable coefficient wave equation with nonlinear damped acoustic boundary conditions abstract we consider a variable coefficient wave equation with nonlinear damped acoustic boundary conditions well posedness in the hadamard sense for strong and weak solutions is proved by using the theory of nonlinear semigroups

multigrid algorithm from cyclic reduction for markovian queueing networks a multigrid method based on cyclic reduction strategy is proposed to solve huge nonsymmetric singular linear systems arising from markovian queueing networks a simple way to construct the matrix dependent prolongation and restriction operators is presented in this paper numerical results for multiple queues are given to illustrate the efficiency and robustness of our methods

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

global existence and global nonexistence of solutions of the cauchy problem for a nonlinearly damped wave equation abstract in this paper we consider the long time behavior of solutions of the initial value problem for semilinear wave equations of the form formula

polynomial decay of a variable coefficient wave equation with an acoustic undamped boundary condition abstract we consider a variable coefficient wave equation with an acoustic undamped condition this is a coupled system of second and first order in time partial differential equations with an acoustic boundary condition on the interface the riemannian geometry method is applied to deal with the variable coefficients under some checkable conditions on the coefficients we obtain the polynomial energy decay

asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions abstract in this paper we consider a multi dimensional wave equation with dynamic boundary conditions related to the kelvin voigt damping global existence and asymptotic stability of solutions starting in a stable set are proved blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained

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

energy decay rate for a von karman system with a boundary nonlinear delay term abstract in this paper we show the energy decay rate for a von karman system with a boundary nonlinear delay term this work is devoted to investigate the influence of kernel function g and the effect of the boundary nonlinear term 1 u t t m 1 u t t a boundary nonlinear time delay term 2 u t t m 1 u t t and prove energy decay rates of solutions when g do not necessarily decay exponentially and the boundary condition has a time delay

an inverse problem for the schrodinger equation with variable coefficients and lower order terms abstract we study the uniqueness and stability for an inverse problem of schrodinger equation with variable coefficients and lower order terms we obtain a carleman estimate by which we recover the potential from partial boundary term

strong stability and uniform decay of solutions to a wave equation with semilinear porous acoustic boundary conditions we consider a wave equation with semilinear porous acoustic boundary conditions this is a coupled system of second and first order in time partial differential equations with possibly semilinear boundary conditions on the interface the results obtained are i strong stability for the linear model ii exponential decay rates for the energy of the linear model and iii local exponential decay rates for the energy of the semilinear model this work builds on a previous result showing generation of a well posed dynamical system the main tools used in the proofs are i the stability theorem of arendt batty ii energy methods used in the study of a wave equation with boundary damping and iii an abstract result of i lasiecka applicable to hyperbolic like systems with nonlinearly perturbed boundary conditions

energy decay for a nonlinear wave equation of variable coefficients with acoustic boundary conditions and a time varying delay in the boundary feedback abstract a variable coefficient wave equation with acoustic boundary conditions and a time varying delay in the boundary feedback is considered applying the riemannian geometry method we show that the decay rates of the nonlinear system with a time varying delay are described by solutions to a first order ode

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

multilevel ilu decomposition in this paper the multilevel ilu mlilu decomposition is introduced during an incomplete gaussian elimination process new matrix entries are generated such that a special ordering strategy yields distinct levels on these levels some smoothing steps are computed the mlilu decomposition exists and the corresponding iterative scheme converges for all symmetric and positive definite matrices convergence rates independent of the number of unknowns are shown numerically for several examples many numerical experiments including unsymmetric and anisotropic problems problems with jumping coefficients as well as realistic problems are presented they indicate a very robust convergence behavior of the mlilu method

a note on optimality in lattice square designs summary this note demonstrates that lattice square designs are a optimal within the class of lattice square designs if and only if they are m s optimal certain restricted lattice square designs are shown to be a optimal

controllability for transmission wave plate equations on riemannian manifolds abstract in this paper we consider controllability for transmission system of coupling wave equations with euler bernoulli equations on riemannian manifolds we show that such a system is exactly controllable by boundary controls only along the exterior boundary which means there is no control on the interface of the transmission system our proofs rely on the hilbert uniqueness method hum and geometric multiplier method

uniform decay of the solution to a wave equation with memory conditions on the boundary abstract a wave equation with variable coefficients in principal part and memory conditions on the boundary is considered the riemannian geometry method is applied to prove the exponential decay of the energy provided the relaxation function also decays exponentially

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

the helmholtz equation in heterogeneous media a priori bounds well posedness and resonances abstract we consider the exterior dirichlet problem for the heterogeneous helmholtz equation i e the equation a u k 2 n u f where both a and n are functions of position we prove new a priori bounds on the solution under conditions on a n and the domain that ensure nontrapping of rays the novelty is that these bounds are explicit in k a n and geometric parameters of the domain we then show that these a priori bounds hold when a and n are l and satisfy certain monotonicity conditions and thereby obtain new results both about the well posedness of such problems and about the resonances of acoustic transmission problems i e a and n discontinuous where the transmission interfaces are only assumed to be c 0 and star shaped the novelty of this latter result is that until recently the only known results about resonances of acoustic transmission problems were for c convex interfaces with strictly positive curvature

global nonexistence theorems for a class of evolution equations with dissipation we study abstract evolution equations with nonlinear damping terms and source terms including as a particular case a nonlinear wave equation of the type ba cl u tt delta u b u t m 2 u t c u p 2 u t x in 0 t times omega 6pt u t x 0 t x in 0 t times partial omega 6pt u 0 cdot u 0 in h 0 1 omega quad u t 0 cdot v 0 in l 2 omega es ea where 0 p 2 m 1 we prove a global nonexistence theorem for positive initial value of the energy when 1 1

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

uniform stability of transmission of wave plate equations with source on riemannian manifold abstract this paper is concerned with the semilinear transmission of wave plate system with source term on riemannian manifold we prove the existence of weak solutions by using faedo galerkin s method furthermore by introducing nonlinear boundary feedbacks acting only on plate we establish the explicit and general decay rates of the system our proofs are based on the geometric multiplier method and the riemannian geometry method

on the approximate cyclic reduction preconditioner we present a preconditioning method for the iterative solution of large sparse systems of equations the preconditioner is based on ideas both from ilu preconditioning and from multigrid the resulting preconditioning technique requires the matrix only a multilevel structure is obtained by using maximal independent sets for graph coarsening a schur complement approximation is constructed using a sequence of point gaussian elimination steps the resulting preconditioner has a transparent modular structure similar to the algorithmic structure of a multigrid v cycle

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

global nonexistence of solutions for a nonlinear wave equation with time delay and acoustic boundary conditions abstract we consider a quasilinear wave equation u t t u t d i v u 2 u d i v u t 2 u t a u t m 2 u t 1 u t x t 2 u t x t b u p 2 u a b 0 associated with initial and dirichlet boundary conditions at one part and acoustic boundary conditions at another part respectively we prove under suitable conditions on m p and for negative initial energy a global nonexistence of solutions