energy decay for a damped nonlinear coupled system this paper proves the well posedness and uniform stabilization of a nonlinear coupled system we estimate the energy decay rate by using the multiplier method

global existence and asymptotic behavior for a coupled hyperbolic system with localized damping abstract in this paper we investigate the global existence and energy decay rate for the solution of a coupled hyperbolic system the semi explicit energy decay rate is established by using piecewise multiplier techniques and weighted integral inequality we extend the energy decay result in alabau boussouira f alabau boussouira convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems appl math optim 51 2005 61 105 for a single equation to the coupled hyperbolic system

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

an extension of mehta theorem with applications abstract a remarkable fundamental theorem established by mehta plays an important role in proving existence of fixed points maximal elements and equilibria in abstract economies in this paper we extend himmelberg s measure of precompactness to the general setting of l c spaces and obtain a generalization of mehta s theorem as an application we develop some new fixed point theorems involving a kind of condensing mappings

uniform stabilization of the wave equation by nonlinear boundary feedback the question of uniformly stabilizing the solution of the wave equation y delta y 0 in omega times 0 infty omega is a bounded domain of bf r n by means of a nonlinear feedback law of the following form is studied partial y partial v k x g y on gamma 0 times 0 infty y 0 on gamma 1 times 0 infty gamma 0 gamma 1 being a suitable partition of the boundary of omega and g a continuous nondecreasing function such that g 0 0 we choose k x in l infty k x geqq 0 such that k x vanishes linearly at the interface points x in bar gamma 0 cap bar gamma 1 then if g s behaves like s p 1 s as s to 0 with p 1 and linearly as s to infty it is proved that the energy of every solution decays like t 2 p 1 as t to infty in the case where p 1 the exponential decay rate is proved

on solutions of the equation a ka the vector differential equation del a ka with k constant appears in models of force free magnetic fields in plasma physics and in astrophysics and also in a model for force free electromagnetic waves solutions of this equation which are identified with physical fields exhibit several inconsistencies this letter identifies the source of these inconsistencies as the lack of covariance of this equation with respect to transformations

energy decay rate for a coupled hyperbolic system with nonlinear damping abstract in this paper we investigate the energy decay rate for the solution of a coupled hyperbolic system the explicit energy decay rate is established by using multiplier techniques and constructing a suitable energy functional

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

general decay rate estimates for viscoelastic dissipative systems abstract the linear viscoelastic equation is considered we prove uniform decay rates of the energy by assuming a nonlinear feedback acting on the boundary without imposing any restrictive growth assumption on the damping term and strongly weakening the usual assumptions on the relaxation function our estimate depends both on the behavior of the damping term near zero and on the behavior of the relaxation function at infinity the proofs are based on the multiplier method and on a general lemma about convergent and divergent series for obtaining the uniform decay rates

fixed point theorems for condensing multimaps on locally g convex spaces abstract in this paper we investigate the fixed point problem for condensing multimaps on locally g convex spaces instead of the usual locally convex topological vector spaces we show that every condensing closed self multimap that has convex values on a nonempty complete convex subset of a locally g convex space has a fixed point some fixed point results for condensing multimaps which have lower semicontinuous l s c cores and applications to abstract economy are also presented

on solutions of curl a ka and force free magnetic fields salingaros has claimed 1986 that solutions of the equation curl a ka k constant for a force free magnetic field are not invariant with respect to gauge transformations and lack covariance with respect to general transformations he has suggested that the force free condition may not be used in physical models however it is shown that the solutions are invariant to gauge transformation and it is argued that solutions of maxwell s equations which satisfy the force free condition locally in a restricted domain are applicable to real physical situations

the equation curl b kb and magnetic fields in two recent letters salingaros has put forward physical arguments to claim that solutions of curl b kb cannot represent real magnetic fields however the first part of his assertions is only a restatement of the well known result that this equation cannot be satisfied everywhere over a non vanishing magnetic field however it does not rule out the use of the equation locally over a restricted region of the field the second part suffers from an incorrect assumption which invalidates his conclusion

collective fixed points and maximal elements with applications to abstract economies abstract in this paper we first establish collective fixed points theorems for a family of multivalued maps with or without assuming that the product of these multivalued maps is condensing as an application of our collective fixed points theorem we derive the coincidence theorem for two families of multivalued maps defined on product spaces then we give some existence results for maximal elements for a family of ls majorized multivalued maps whose product is condensing we also prove some existence results for maximal elements for a family of multivalued maps which are not ls majorized but their product is condensing as applications of our results some existence results for equilibria of abstract economies are also derived the results of this paper are more general than those given in the literature

long time behavior of a coupled heat wave system arising in fluid structure interaction this paper is devoted to the analysis of the long time behavior of a coupled wave heat system in which a wave and a heat equation evolve in two bounded domains with natural transmission conditions at a common interface these conditions couple in particular the heat unknown with the velocity of the wave solution this model may be viewed as a simplified version of linearized models which arise in fluid structure interaction first we show the strong asymptotic stability of solutions to this system then based on the construction of ray like solutions by means of geometric optics expansions and a careful analysis of the transfer of energy at the interface we show the lack of uniform decay in general domains further we obtain a polynomial decay result for smooth solutions of the system under a suitable geometric assumption which guarantees that the heat domain envelopes the wave domain finally in the absence of geometric conditions we show a logarithmic decay result for the same system but with simplified transmission conditions at the interface we also analyze the difficulty there is to extend this result to the more natural transmission conditions

equilibria of non compact generalized games with l majorized preference correspondences an existence theorem of maximal elements in a non compact set for l majorized correspondences is obtained next an existence theorem of an equilibrium in a qualitative game is proved and is then applied to achieve an existence theorem of equilibrium in a non compact abstract economy with l majorized preference correspondences these results are either very closely related to or generalizations of those recent results of borglin keiding yannelis prabhakar toussaint and tulcea

quadratic optimization for infinite dimensional linear differential difference type systems syntheses via the fredholm equation a closed loop solution for quadratic optimization is presented for control systems whose model is given by infinite dimensional linear differential difference equations frac dx t dt ax t sum i 1 n a i x left t h i right bu t sum j 1 m b j u left t r j right a nonsemigroup evolution formula for the fundamental solution is given first the system is then reduced to a volterra integral system by the semicausality approach a new optimality principle is established and the closed loop optimal control is given by real time state feedback plus retarded state integral feedback the feedback operator is determined by solving a linear fredholm integral equation the two crucial methods semicausal dynamical optimization for volterra integral systems and nonsemigroup evolution property are brought together to generalize the syntheses results to infinite dimensional cases

on solutions of the equation a ka ii the magnetic force free model for pt i see ibid vol 19 l101 4 1986 solutions of the vector differential equation del a ka k constant not 0 have been shown not to correspond to physical magnetic fields this is true even though they are solenoidal del a 0 which is a necessary but not sufficient condition for a vector field to be a magnetic field here the magnetic force free model is very carefully analysed and the inapplicability of the above equation is demonstrated using physical arguments

long time behavior of solutions to a nonlinear hyperbolic relaxation system abstract we study the large time behavior of solutions of a one dimensional hyperbolic relaxation system that may be written as a nonlinear damped wave equation first we prove the global existence of a unique solution and their decay properties for sufficiently small initial data we also show that for some large initial data solutions blow up in finite time for quadratic nonlinearities we prove that the large time behavior of solutions is given by the fundamental solution of the viscous burgers equation in some other cases the convection term is too weak and the large time behavior is given by the linear heat kernel

decay estimates for second order evolution equations with memory abstract this paper develops a unified method to derive decay estimates for general second order integro differential evolution equations with semilinear source terms depending on the properties of convolution kernels at infinity we show that the energy of a mild solution decays exponentially or polynomially as t our approach is based on integral inequalities and multiplier techniques these decay results can be applied to various partial differential equations we discuss three examples a semilinear viscoelastic wave equation a linear anisotropic elasticity model and a petrovsky type system

on solutions to the equation a ka in a recent letter salingaros ibid vol 19 l101 4 1986 claimed that the equation curl a ka cannot be used to describe a magnetic field b a he bases this on the assertion that the magnetic field b caused by a current density j must be orthogonal to j this assertion is shown to be incorrect