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

exact order of hoffman s error bounds for elliptic quadratic inequalities derived from vector valued chebyshev approximation in this paper we introduce the exact order of hoffman s error bounds for approximate solutions of elliptic quadratic inequalities elliptic quadratic inequalities are closely related to chebyshev approximation of vector valued functions including complex valued functions the set of chebyshev approximations of a vector valued function defined on a finite set is shown to be hausdorff strongly unique of order exactly 2 s for some nonnegative integer s as a consequence the exact order of hoffman s error bounds for approximate solutions of elliptic quadratic inequalities is exactly 2 s for some nonnegative integer s the integer s called the order of deficiency which is computable quantifies how much the abadie constraint qualification is violated by the elliptic quadratic inequalities

error bounds for piecewise convex quadratic programs and applications in this paper we establish a local error estimate for feasible solutions of a piecewise convex quadratic program and a global error estimate for feasible solutions of a convex piecewise quadratic program these error estimates provide a unified approach for deriving many old and new error estimates for linear programs linear complementarity problems convex quadratic programs and affine variational inequality problems the approach reveals the fact that each error estimate is a consequence of some reformulation of the original problem as a piecewise convex quadratic program or a convex piecewise quadratic program in a sense even robinson s result on the upper lipschitz continuity of a polyhedral mapping can be considered as a special case of error estimates for approximate solutions of a piecewise convex quadratic program as an application we derive new global error estimates for iterates of the proximal point algorithm for solving a convex piecewise quadratic program

exact boundary observability for nonautonomous quasilinear wave equations abstract by means of a direct and constructive method based on the theory of semiglobal c 2 solution the local exact boundary observability is shown for nonautonomous 1 d quasilinear wave equations the essential difference between nonautonomous wave equations and autonomous ones is also revealed

analysis of a model of stage structured population dynamics growth with time state dependent time delay the main purpose of this paper is to analyze a model of stage structured population growth where age to maturity is state dependent we found that a positive equilibrium always exists criteria for stability is obtained

boundary exact controllability of interface problems with singularities ii addition of internal controls we prove the exact controllability by boundary action of hyperbolic interface problems with singularities the two proposed methods consist of acting by a classical boundary control whose support does not contain a neighborhood of the singular points and adding internal controls located near these singular points see m t niane and o seck c r acad sci paris ser i 318 1994 pp 945 948 a heibig and m moussaoui disc cont dynam syst 2 1996 pp 367 386 m t niane and o seck c r acad sci paris ser i 316 1993 pp 695 700 where such a method was introduced

a new stage structured predator prey gomportz model with time delay and impulsive perturbations on the prey abstract in this paper we formulate a robust prey dependent consumption predator prey gomportz model with periodic harvesting catching or poisoning for the prey and stage structure for the predator with constant maturation time delay through stage time delay and perform a systematic mathematical and ecological study by use of the discrete dynamical system determined by the stroboscopic map we obtain a predator extinction periodic solution further we show it is globally attractive when some parameters of the system are under appropriate conditions by using the theory on delay functional and impulsive differential equation we obtain sufficient condition with time delay for the permanence of the system in this paper the main feature is that we introduce time delay and pulse into the predator prey natural enemy pest model with stage structure exhibit a new modeling method which is applied to investigate delay impulsive differential equations and give some reasonable suggestions for pest management

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

error estimates and lipschitz constants for best approximation in continuous function spaces abstract we use a structural characterization of the metric projection pg f from the continuous function space to its one dimensional subspace g to derive a lower bound of the hausdorff strong unicity constant or weak sharp minimum constant for pg and then show this lower bound can be attained then the exact value of lipschitz constant for pg is computed the process is a quantitative analysis based on the g teaux derivative of pg a representation of local lipschitz constants the equivalence of local and global lipschitz constants for lower semicontinuous mappings and construction of functions

complex chebyshev approximation for fir digital filters an adaptive approach to fir finite impulse response filter design is applied to a fully general complex specification showing it to be capable of giving an optimum chebyshev solution it is thought to be one of the first practical approaches to achieve this in the case of a complex function design examples include a bandpass filter with nearly linear phase and all pass filters with general shaping phase comparisons are drawn with equivalent results from other algorithms

stability of a competition model with two stage structure a population model with stage structure which describes the competition of two species for space is considered the model is established under the assumptions that reproductive rates of two species are affected by competition and that the space occupied by one type of juveniles cannot be neglected estimates on the length of delays for which positive equilibrium of the model remains stable are given sufficient conditions are also derived that ensure global stability of positive equilibrium

asymptotic behaviors of competitive lotka volterra system with stage structure in this paper a two species competitive model with stage structure is presented and studied results on the global extinction and permanence are given which generalize the well known three theorems for the two species competitive system and moreover they confirm the negative effect of stage structure on the permanence of populations as well as estimate the degree of such effect conclusions in this paper suggest that for a competitive community stage structure is also one of the important reasons that cause permanence and extinction

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

the asymptotic behaviors of a stage structured autonomous predator prey system with time delay abstract in this paper we consider an autonomous predator prey lotka volterra system in which individuals in the population may belong to one of two classes the immatures and the matures the age to maturity is represented by a time delay by using eigenvalue analysis principal term analyze method reduction to absurdity and iterative method we obtain some simple conditions for global asymptotic stability of the unique positive equilibrium point moreover a condition that the prey population in the system get extinction and the predator population in the system get permanence will be obtained meanwhile the theorems extend the corresponding conclusions in which there have no two stage structures

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

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

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

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

nonlinear boundary stabilization for a transmission problem in elasticity in this article we study the uniform stability for the solutions of a transmission problem in non homogeneous anisotropic elasticity we consider a boundary dissipation given for a frictional damping and explicit rates of decay are obtained

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

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

design of fir filters in the complex domain the design of fir digital filters with a complex valued desired frequency response using the chebyshev error is investigated the complex approximation problem is converted into a real approximation problem which is nearly equivalent to the complex problem a standard linear programming algorithm for the chebyshev solution of overdetermined equations is used to solve the real approximation problem additional constraints are introduced which allow weighting of the phase and or group delay of the approximation digital filters are designed which have nearly constant group delay in the passbands the desired constant group delay which gives the minimum chebyshev error is found to be smaller than that of a linear phase filter of the same length these filters in addition to having a smaller approximately constant group delay have better magnitude characteristics than exactly linear phase filters with the same length the filters have nearly equiripple magnitude and group delay

error bounds for convex differentiable inequality systems in banach spaces the paper is devoted to studying the hoffman global error bound for convex quadratic affine inequality equality systems in the context of banach spaces we prove that the global error bound holds if the hoffman local error bound is satisfied for each subsystem at some point of the solution set of the system under consideration this result is applied to establishing the equivalence between the hoffman error bound and the abadie qualification condition as well as a general version of wang pang s result 30 on error bound of holderian type the results in the present paper generalize and unify recent works by luo luo in 17 li in 16 and wang pang in 30

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

extension of hoffman s error bound to polynomial systems given any linear system defined by linear inequalities equalities in re n hoffman s error bound says that the distance from any point x in re n to the solution set of the linear system is bounded by a constant independent of x times a certain residual function evaluated at x this paper considers arbitrary possibly nonconvex polynomial systems defined by polynomial inequalities equalities it is shown that the solution sets of such systems are in general holder continuous as the right hand side changes in contrast to the lipschitzian continuity for the linear case also for any convex quadratic inequality system possessing an interior solution the authors show that its solution set behaves in a lipschitzian manner as the right hand side varies this result sharpens the earlier error bound results by mangasarian and robinson for general convex differentiable inequality systems which in addition to the interiority assumption require either an asymptotic constraint qualification con

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

observability inequalities for the transmission of shallow shells in this paper we establish some observability inequalities from both boundary and distributed controls for the transmission of shallow shell with a middle surface of any shape in particular if only the boundary controls are allowed we obtain the condition for the observability inequality on young s modulus and poisson s coefficient of the material which is similar as those in the case of wave and plate equations

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

a nonautonomous predator prey system with stage structure and double time delays in the present paper we study a nonautonomous predator prey model with stage structure and double time delays due to maturation time for both prey and predator we assume that the immature and mature individuals of each species are divided by a fixed age and the mature predator only attacks the immature prey based on some comparison arguments we discuss the permanence of the species by virtue of the continuation theorem of coincidence degree theory we prove the existence of positive periodic solution by means of constructing an appropriate lyapunov functional we obtain sufficient conditions for the uniqueness and the global stability of positive periodic solution two examples are given to illustrate the feasibility of our main results

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

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

stabilization and controllability for the transmission wave equation we address the problem of control of the transmission wave equation in particular we consider the case where due to total internal reflection of waves at the interface the system may not be controlled from exterior boundaries we show that such a system can be controlled by introducing both boundary control along the exterior boundary and distributed control near the transmission boundary and give a physical explanation why the additional control near the transmission boundary might be needed for some domains

a stage structured predator prey model of beddington deangelis type we formulate and study a robust stage structured predator prey model of beddington deangelis type functional response the time delay is the time taken from birth to maturity the beddington deangelis functional response is similar to the holling type 2 functional response but contains an extra term describing mutual interference by predators first we show that the predator coexists with prey permanently if and only if the predator s recruitment rate at the peak of prey abundance is larger than its death rate second we show that if the system is permanent then a sufficiently large degree of the predator interference can not only stabilize the system but also guarantee the stability of the system against the increase of the carrying capacity of prey and the increase of birth rate of the adult predator third we show both analytically and numerically that stability switches of interior equilibrium may occur as maturation time delay increases stability may change from stable to unstable to finally stable implying that a large delay can be stabilizing

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

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

permanence of general stage structured consumer resource models much of the existing stage structured consumer resource models ignore the permanence in this paper we consider the permanence for a series of staged structured consumer resource models with the function response of so called prey dependence resource dependence type we show that the systems are permanent if and only if the adult consumer s recruitment rate at the peak of resource abundance is more than its death rate our results indicate that the large consumer s maturation time delay will directly lead to its extinction furthermore our arguments for the main results give a light for permanence in the general stage structured consumer resource systems

observability inequalities for shallow shells we consider some observability inequalities from boundary for a general shallow shell with a middle surface of any shape at first an estimate is established by the geometric multiplier method in the case that no boundary conditions are imposed under some checkable geometric conditions then our results yield continuous observability estimates for two kinds of boundary conditions which have a physical meaning with an explicit observability time and hence by duality exact controllability results

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

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

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

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

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

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

on the design of fir filters by complex chebyshev approximation the long standing problem of approximating a complex valued desired function with a finite impulse response fir filter is considered it is formulated as an equalization to be solved using complex valued filters the proposed algorithm deals directly with the complex error function which depends linearly on the coefficients of the filter to be designed the magnitude of this error function is minimized in the chebshev sense using a generalization of the remez exchange algorithm the method can be used to design complex or real valued selective systems as well the well known design of optimal fir filters with linear phase is included here as a special case

a predator prey system with stage structure for predator abstract this paper studies the asymptotoc behavior of a predator prey model with stage structure it is found that an orbitally asymptotically stable periodic orbit exists in that model when time delay due to gestation of predator and time delay from crowding effect of prey are incorporated we establish the condition for the permanence of populations and sufficient conditions under which positive equilibrium of the model is globally stable

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

a class of nonlinear diffusion problems in age dependent population dynamics in this paper we study the existence the uniqueness and the asymptotic behaviour of a class of nonlinear diffusion problems these problems are motivated by models of age dependent population dynamics which originate in the article by gurtin maccamy ll only a few special cases of these models have been analyzed to date with the most recent published work being that of maccamy 17 gurtin maccamy 12 and langlais 15 161 the cases treated in 12 171 are restricted to special simple forms of the birth and death moduli that occur in these models and to a specific form of the nonlinear diffusion mechanism on the other hand langlais 16 considers a different nonlinear diffusion mechanism and obtains a type of generalized solution for general forms of the birth and death moduli in this work we consider a general form of the nonlinear diffusion mechanism and we develop a method for establishing the existence and uniqueness of solutions of the resulting equations our method allows us to obtain classical solutions even with general forms of the birth and death moduli we also describe the asymptotic behaviour of the solutions when the time variable becomes large and apply our results to some specific examples the equations that we study are motivated as follows consider a population that can disperse in a spatial domain r for simplicity we take q j where j is an open interval in r but it will be clear from the context that more general regions q of r can be considered let a t x denote the number of individuals per unit length and unit age that are of age a at time t and are located at the position x e j the total population per unit length at time t and at position x is given by

stabilization of transmission coupled wave and euler bernoulli equations on riemannian manifolds by nonlinear feedbacks abstract we consider the transmission system of coupling wave equations with euler bernoulli equations on riemannian manifolds by introducing nonlinear boundary feedback controls we establish the exponential and rational energy decay rate for the problem our proofs rely on the geometric multiplier method

a degenerate nonlinear diffusion problem in age structured population dynamics we consider a degenerate nonlinear diffusion problem that arises in the modelling of agestructured populations the derivation of such problems has been discussed in a variety of places see 4 5 7 f or example and we give only a brief description of the motivation for the equations we treat the particular problem that we consider is discussed by maccamy 7 who also analyses a special case of the resulting equations our treatment of this problem is based on the general method we developed in l 2 combined with variants of ideas and techniques used by ladyshenskaya 6 maccamy 7 olienik 8 and sabinina 9 the problem is as follows let a denote chronological age f denote time and x denote spatial position and let a t x denote the number of individuals per unit age and unit length who are of age a at time t and at position x here we take a t x e 0 a x o tl x 0 1 by fl q and pc a we denote the death rate and the birth rate per unit age of individuals of age a the total population density per unit length at time t is

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

finite termination of the proximal point algorithm this paper concerns the notion of a sharp minimum on a set and its relationship to the proximal point algorithm we give several equivalent definitions of the property and use the notion to prove finite termination of the proximal point algorithm