the cauchy problem in one dimensional nonlinear viscoelasticity abstract the initial value problem for a nonlinear hyperbolic volterra equation which models the motion of an unbounded viscoelastic bar is studied under physically motivated assumptions the existence of a unique globally defined classical solution is established provided the initial data are sufficiently smooth and small boundedness and asymptotic behavior are also discussed this analysis is based on energy estimates in conjunction with properties of strongly positive definite kernels

decay property for second order hyperbolic systems of viscoelastic materials we study a class of second order hyperbolic systems with dissipation which describes viscoelastic materials the considered dissipation is given by the sum of the memory term and the damping term when the dissipation is effective over the whole system we show that the solution decays in l 2 at the rate t n 4 as t provided that the corresponding initial data are in l 2 l 1 w heren is the space dimension the proof is based on the energy method in the fourier space also we discuss similar systems with weaker dissipation by introducing the operator 1 2 with 0 in front of the dissipation terms and

weak solutions of a class of quasilinear hyperbolic integro differential equations describing viscoelastic materials global weak solutions of scalar second order quasilinear hyperbolic integro differential equations with singular kernels are constructed perturbations of rest states are shown to propagate with finite speed smoothing effects of the solution operator are exhibited and conditions for the asymptotic stability of rest states are given the equations arise in viscoelasticity

a decay result to a viscoelastic problem in rn with an oscillating kernel in this paper we consider a linear cauchy viscoelastic problem we show that for compactly supported initial data and for not necessarily decreasing oscillating relaxation function the decay of the first energy of solutions is polynomial the proof relies on some appropriately chosen functionals the combination of which satisfies a certain integral inequality

nonlinear stability of rarefaction waves for a viscoelastic material with memory in this paper we will discuss the stability of rarefaction waves for a viscoelastic material with memory the rarefaction waves for which the sta bility is tested are not themselves solutions to the integrodifferential equations 1 1 governing the viscoelastic material they are solutions to a related equi librium system of conservation laws given by 1 11 we shall show that if the forcing term and the past history are small and if the initial data are close to the rarefaction waves the solutions to 1 1 will approach the rarefaction waves in sup norm as the time goes to infinity j oo with the initial data u x 0 v x 0 u0 x v0 x xer l2 lim uo x v0 x u v x oo

solutions of fractional logistic equations by euler s numbers abstract in this paper we solve in the convergence set the fractional logistic equation making use of euler s numbers to our knowledge the answer is still an open question the key point is that the coefficients can be connected with euler s numbers and then they can be explicitly given the constrained of our approach is that the formula is not valid outside the convergence set the idea of the proof consists to explore some analogies with logistic function and euler s numbers and then to generalize them in the fractional case

learning by distances a model of learning by distances is presented in this model a concept is a point in a metric space at each step of the learning process the student guesses a hypothesis and receives from the teacher an approximation of its distance to the target a notion of a distance measuring the proximity of a hypothesis to the correct answer is common to many models of learnability by focusing on this fundamental aspect we discover some general and simple tools for the analysis of learnability tasks as a corollary we present new learning algorithms for valiant s pac scenario with any given distribution these algorithms can learn any pac learnable class and in some cases settle for significantly less information than the usual labeled examples insight gained by the new model is applied to show that every class of subsets c that has a finite vc dimension is pac learnable with respect to any fixed distribution previously known results of this nature were subject to complicated measurability constraints

remarks on the global sobolev inequalities in the minkowski space rn 1 on demontre des inegalites de sobolev globales sur l espace de minkowski r n 1 le theoreme principal est valable sur des tranches a temps fixe

uniform stability of semilinear wave equations with arbitrary local memory effects versus frictional dampings abstract this paper is concerned with the mixed initial boundary value problem for semilinear wave equations with complementary frictional dampings and memory effects we successfully establish uniform exponential and polynomial decay rates for the solutions to this initial boundary value problem under much weak conditions concerning memory effects more specifically we obtain the exponential and polynomial decay rates after removing the fundamental condition that the memory effect region includes a part of the system boundary while the condition is a necessity in the previous literature moreover for the polynomial decay rates we only assume minimal conditions on the memory kernel function g without the usual assumption of g controlled by g

asymptotic stability of abstract dissipative systems with infinite memory we consider in this paper the problem of asymptotic behavior of solutions to an abstract linear dissipative integrodifferential equation with infinite memory past history modeling linear viscoelasticity we show that the stability of the system holds for a much larger class of the convolution kernels than the one considered in the literature and we provide a relation between the decay rate of the solutions and the growth of the kernel at infinity some applications are also given

temps de vie des solutions regulieres des equations d euler compressibles axisymetriques en dimension deux nous considerons le systeme des equations d euler isentropiques en dimension deux pour des donnees initiales invariantes par rotation et perturbations de taille e d un etat de repos on etablit un equivalent du temps de viet e de la solution classique lim 2 t 2 de plus on donne pour t leqq frac a 2 varepsilon 2 a tau une estimation de la vraie solution en calculant la taille de son ecart a une solution approchee construite dans un precedent travail

attractors for wave equations with degenerate memory abstract this paper is concerned with the long time dynamics of a semilinear wave equation with degenerate viscoelasticity u t t u 0 g s div a x u t s d s f u h x defined in a bounded domain of r 3 with dirichlet boundary condition and nonlinear forcing f u with critical growth the problem is degenerate in the sense that the function a x 0 in the memory term is allowed to vanish in a part of when a x does not degenerate and g decays exponentially it is well known that the corresponding dynamical system has a global attractor without any extra dissipation in the present work we consider the degenerate case by adding a complementary frictional damping b x u t which is in a certain sense arbitrarily small such that a b 0 in despite that the dissipation is given by two partial damping terms of different nature none of them necessarily satisfying a geometric control condition we establish the existence of a global attractor with finite fractal dimension

global solutions to the equation of viscoelasticity with fading memory abstract we consider the initial history value problem for the one dimensional equation of thermoelasticity with fading memory it is proved that if the data are smooth and small then a unique smooth solution exists globally in time and converges to the constant equilibrium state as time goes to infinity our proof is based on a technical energy method which makes use of the strict convexity of the entropy function and the properties of strongly positive definite kernels

weak solutions of hyperbolic parabolic volterra equations the existence of a global weak solution satisfying certain a priori l bounds of the equation ut t x ft k t s a ux x s x ds f t x is established the kernel k is locally integrable and log convex and a has only one local minimum which is positive introduction the purpose of this paper is to establish the existence of a global weak solution of the equation 1 t ut t x k k t s a ux x s x ds f t x t o x e 0 1 u o x uo x x e o 1 u t o u t 1 o t o where the subscripts denote differentiation with respect to the corresponding variables and to show that this weak solution satisfies certain a priori l bounds equation 1 is of interest because it appears in mathematical models of viscoelasticity see 18 and 31 but also because it is of a form somewhere between a parabolic and a hyperbolic equation this is due to the fact that when k 1 we get the nonlinear wave equation utt t x a ux x t x ft t x and if on the other hand k is replaced by the delta functional then we get the nonlinear diffusion equation ut t x a ux x t x f t x the nonlinear wave equation that corresponds to the completely elastic case in mechanics has a weak solution with both ux and ut bounded and initially smooth solutions develop singularities in the derivatives in finite time the received by the editors september 22 1992 1991 mathematics subject classification primary 45k05 secondary 45d05 45n05 35k99 35l99 73f99

blowup for the 3d compressible euler equations abstract we establish several results about the blowup of the solutions for the cauchy problem of the 3d compressible euler equations under some assumptions on weighed functionals associated with the initial momentum that they are large enough to develop singularities especially we prove the blowup results without the condition 0 x 0 e s x 0 e s d x 0 while it is an essential condition in the well known result obtained by thomas c sideris

the decay rate for a fractional differential equation abstract we consider the fractional differential equation u tt t x 0 t k t s u sxx s x ds u xx t x t 0 x 0 1 with dirichlet boundary conditions and initial values this problem with a particular kernel may be looked at as an internally damped wave equation with a strong damping of order less than one it is proved that the solution of this problem with a weakly singular kernel decays exponentially to zero

a variational formulation of the perturbed motion problem for a viscoelastic body abstract the analysis of perturbed motion is often very important for studying the progress of strain and stress in viscoelastic bodies the authors intend to provide a variational formulation of the problem as an alternative to the differential formulation used to date by solving the so called inverse problem of the calculus of variations this paper shows how the operator ruling the problem can be made symmetric by using a convolution bilinear form to obtain four functionals which are stationary at the solution of the differential problem in conclusion for example the two dimensional equations of the perturbed motion of a viscoelastic thin plate are derived from the stationary condition of the three dimensional functional

the longtime behavior of a nonlinear reissner mindlin plate with exponentially decreasing memory kernels abstract in this paper we investigate the longtime behavior of the mathematical model of a homogeneous viscoelastic plate based on reissner mindlin deformation shear assumptions according to the approximation procedure due to lagnese for the kirchhoff viscoelastic plate the resulting motion equations for the vertical displacement and the angle deflection of vertical fibers are derived in the framework of the theory of linear viscoelasticity assuming that in general both lame s functions and depend on time the coupling terms between the equations of displacement and deflection depend on hereditary contributions we associate to the model a nonlinear semigroup and show the behavior of the energy when time goes on in particular assuming that the kernels and decay exponentially and not too weakly with respect to the physical properties considered in the model then the energy decays uniformly with respect to the initial conditions i e we prove the existence of an absorbing set for the semigroup associated to the model

on the decay of solutions in nonsimple elastic solids with memory the decay of solutions in nonsimple elasticity with memory is addressed analyzing how the decay rate is influenced by the different dissipation mechanisms appearing in the equations in particular a first order dissipation is shown to guarantee the asymptotic stability of the related solution semigroup but is not strong enough to entail exponential stability the latter occurs for a dissipation mechanism of the second order that is the same order as the one of the leading operator

on the uniform decay in viscoelastic problems in rn in this paper we consider a linear cauchy viscoelastic problem we show that for compactly supported initial data and for an exponentially decaying relaxation function the decay of the first energy of solution is polynomial the finite speed propagation is used to compensate for the lack of poincare s inequality in r n

blow up of a hyperbolic equation of viscoelasticity with supercritical nonlinearities abstract we investigate a hyperbolic pde modeling wave propagation in viscoelastic media under the influence of a linear memory term of boltzmann type and a nonlinear damping modeling friction as well as an energy amplifying supercritical nonlinear source u t t k 0 u 0 k s u t s d s u t m 1 u t u p 1 u in 0 t u x t u 0 x t in 0 where is a bounded domain in r 3 with a dirichlet boundary condition the relaxation kernel k is monotone decreasing and k 1 we study blow up of solutions when the source is stronger than dissipations i e p max m k 0 under two different scenarios first the total energy is negative and the second the total energy is positive with sufficiently large quadratic energy this manuscript is a follow up work of the paper 30 in which hadamard well posedness of this equation has been established in the finite energy space the model under consideration features a supercritical source and a linear memory that accounts for the full past history as time goes to which is distinct from other relevant models studied in the literature which usually involve subcritical sources and a finite time memory

on a class of quasilinear partial integrodifferential equations with singular kernels abstract we prove local and global existence theorems for a model equation in nonlinear viscoelasticity in contrast to previous studies we allow the memory function to have a singularity we approximate the equation by equations with regular kernels and use energy estimates to prove convergence of the approximate solutions

nonlinear stability of travelling wave solutions for viscoelastic materials with fading memory abstract in this paper we shall discuss the stability of smooth monotone travelling wave solutions for viscoelastic materials with memory it is known that a smooth monotone travelling wave solution exists for 1 1 if the end states are close and satisfy the rankine hugoniot condition for such a travelling wave we shall show that if the initial data are close to a travelling wave solution the solutions to 1 1 will approach the travelling wave solution in sup norm as the time goes to infinity for the constitutive relations we shall discuss two cases convex and nonconvex

a complete global solution to the pressure gradient equation abstract we study the domain of existence of a solution to a riemann problem for the pressure gradient equation in two space dimensions the riemann problem is the expansion of a quadrant of gas of constant state into the other three vacuum quadrants the global existence of a smooth solution was established in dai and zhang z dai t zhang existence of a global smooth solution for a degenerate goursat problem of gas dynamics arch ration mech anal 155 2000 277 298 up to the free boundary of vacuum we prove that the vacuum boundary is the coordinate axes

stochastic nonlinear wave equation with memory driven by compensated poisson random measures in this paper we study a class of stochastic nonlinear wave equation with memory driven by levy noise we first show the existence and uniqueness of global mild solutions using a suitable energy function second under some additional assumptions we prove the exponential stability of the solutions

random attractors for damped non autonomous wave equations with memory and white noise abstract we first prove the existence of random attractors for the continuous random dynamical systems generated by stochastic damped non autonomous wave equations with linear memory and additive white noise when the nonlinearity has a critically growing exponent then we study the upper semicontinuity of random attractors when the coefficient of random term approaches zero

a general lower bound on the number of examples needed for learning abstract we prove a lower bound of 1 ln 1 vcdim c on the number of random examples required for distribution free learning of a concept class c where vcdim c is the vapnik chervonenkis dimension and and are the accuracy and confidence parameters this improves the previous best lower bound of 1 ln 1 vcdim c and comes close to the known general upper bound of o 1 ln 1 vcdim c ln 1 for consistent algorithms we show that for many interesting concept classes including k cnf and k dnf our bound is actually tight to within a constant factor

learnability and the vapnik chervonenkis dimension valiant s learnability model is extended to learning classes of concepts defined by regions in euclidean space e n the methods in this paper lead to a unified treatment of some of valiant s results along with previous results on distribution free convergence of certain pattern recognition algorithms it is shown that the essential condition for distribution free learnability is finiteness of the vapnik chervonenkis dimension a simple combinatorial parameter of the class of concepts to be learned using this parameter the complexity and closure properties of learnable classes are analyzed and the necessary and sufficient conditions are provided for feasible learnability

weak stability for coupled wave and or petrovsky systems with complementary frictional damping and infinite memory abstract in this paper we consider coupled wave wave petrovsky petrovsky and wave petrovsky systems in n dimensional open bounded domain with complementary frictional damping and infinite memory acting on the first equation we prove that these systems are well posed in the sense of semigroups theory and provide a weak stability estimate of solutions where the decay rate is given in terms of the general growth of the convolution kernel at infinity and the arbitrary regularity of the initial data we finish our paper by considering the uncoupled wave and petrovsky equations with complementary frictional damping and infinite memory and showing a strong stability estimate depending only on the general growth of the convolution kernel at infinity

decay estimate and asymptotic profile for a plate equation with memory abstract in this paper the initial value problem for a plate equation with a memory is considered under weaker assumptions on the memory function we obtain the decay estimates of solutions which is of the regularity loss type by applying the energy method in fourier space moreover if the memory kernel is an exponential function we derive the large time behavior and asymptotic profile of solutions in the one dimensional space by virtue of the technique of spectral analysis

spectral analysis and exponential stability of one dimensional wave equation with viscoelastic damping abstract this paper presents the exponential stability of a one dimensional wave equation with viscoelastic damping using the asymptotic analysis technique we prove that the spectrum of the system operator consists of two parts the point and continuous spectrum the continuous spectrum is a set of n points which are the limits of the eigenvalues of the system and the point spectrum is a set of three classes of eigenvalues one is a subset of n isolated simple points the second is approaching to a vertical line which parallels to the imagine axis and the third class is distributed around the continuous spectrum moreover the riesz basis property of the generalized eigenfunctions of the system is verified consequently the spectrum determined growth condition holds true and the exponential stability of the system is then established

integro differential equations of hyperbolic type with positive definite kernels abstract the main purpose of this work is to study the damping effect of memory terms associated with singular convolution kernels on the asymptotic behavior of the solutions of second order evolution equations in hilbert spaces for kernels that decay exponentially at infinity and possess strongly positive definite primitives the exponential stability of weak solutions is obtained in the energy norm it is also shown that this theory applies to several examples of kernels with possibly variable sign and to a problem in nonlinear viscoelasticity

the concept of a minimal state in viscoelasticity new free energies and applications to pdes we show here the impact on the initial boundary value problem and on the evolution of viscoelastic systems of the use of a new definition of state based on the stress response see e g 48 16 41 comparisons are made between this new approach and the traditional one which is based on the identification of histories and states we shall refer to a stress response definition of state as the minimal state 29 materials with memory and with relaxation are discussed the energetics of linear viscoelastic materials is revisited and new free energies expressed in terms of the minimal state descriptor are derived together with the related dissipations furthermore both the minimum and the maximum free energy are recast in terms of the minimal state variable and the current strain the initial boundary value problem governing the motion of a linear viscoelastic body is re stated in terms of the minimal state and the velocity field through the principle of virtual power the advantages are i the elimination of the need to know the past strain history at each point of the body and ii the fact that initial and boundary data can now be prescribed on a broader space than resulting from the classical approach based on histories these advantages are shown to lead to natural results about well posedness and stability of the motion finally we show how the evolution of a linear viscoelastic system can be described through a strongly continuous semigroup of linear contraction operators on an appropriate hilbert space the family of all solutions of the evolutionary system obtained by varying the initial data in such a space is shown to have exponentially decaying energy

blowup of small data solutions for a quasilinear wave equation in two space dimensions for the quasilinear wave equation 2 t ui u ututt we analyze the long time behavior of classical solutions with small not rotationally invariant data we give a complete asymptotic expansion of the lifespan and describe the solution close to the blowup point it turns out that this solution is a blowup solution of cusp type according to the terminology of the author 3

on the blowup of classical solutions to the 3 d pressure gradient systems the 3 d pressure gradient system arises from the splitting of the three dimensional compressible euler system which can be reduced into such a nonlinear wave equation t2v div ev v 0 where div ev v i 13 i ev iv i xi 1 i 3 and x x1 x2 x3 in this paper we will establish a blowup result of classical solutions to the 3 d pressure gradient systems when the initial data are of small perturbations with respect to constant states

error estimates for finite volume approximations of classical solutions for nonlinear systems of hyperbolic balance laws we consider a general class of finite volume schemes on unstructured but quasi uniform meshes for first order systems of hyperbolic balance laws on unstructured meshes provided the system is equipped with at least one entropy entropy flux tuple and the associated cauchy problem allows for a classical solution u we give conditions such that the finite volume approximation u h converges to u if the mesh parameter h tends to zero in fact we prove an error estimate of the form u u h l 2 le c sqrt h where c is independent of h the proof relies on a stability result for classical solutions in the class of entropy solutions due to dafermos arch rational mech anal 94 1979 pp 373 389 and diperna indiana univ math j 28 1979 pp 137 188 finally we present examples such that the conditions to apply the general convergence estimate can be satisfied at least in part the examples cover general scalar equations weakly coupled systems and the system of elastodynamics in one dimension moreover we generalize the concept of entropy conservative methods due to tadmor math comp 49 1987 pp 91 103 and show how this can be used to establish the convergence of finite volume methods for the system s case

global existence and asymptotic decay of solutions to the nonlinear timoshenko system with memory abstract in this paper we consider the initial value problem for the nonlinear timoshenko system with a memory term due to the regularity loss property and weak dissipation we have to assume stronger nonlinearity than usual by virtue of the semi group arguments we obtain the global existence and optimal decay of solutions to the nonlinear problem under smallness and enough regularity assumptions on the initial data where we employ a time weighted l 2 energy method combined with the optimal l 2 decay of lower order derivatives of solutions

nonlinear waves for viscoelasticity with fading memory abstract nonlinear waves for a model of viscoelastic materials are constructed and analyzed there are traveling waves expansion waves and diffusion waves the stress in the model depends on the present strain as well as its past history traveling waves are studied based on the admissibility criterion for the models with equilibrium or instantaneous elastic response expansion waves and diffusion waves are constructed in the time asymptotic sense asymptotic states with given end states are constructed and consist of these elementary waves

hadamard well posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping abstract presented here is a study of a viscoelastic wave equation with supercritical source and damping terms we employ the theory of monotone operators and nonlinear semigroups combined with energy methods to establish the existence of a unique local weak solution in addition it is shown that the solution depends continuously on the initial data and is global provided the damping dominates the source in an appropriate sense

existence and decay of solutions of a viscoelastic equation with a nonlinear source abstract in a bounded domain we consider u tt u 0 t g t u d u u where 0 and g is a nonnegative and decaying function we prove a local existence theorem and show for certain initial data and suitable conditions on g and that this solution is global with energy which decays exponentially or polynomially depending on the rate of the decay of the relaxation function g

the small data solutions of general 3 d quasilinear wave equations ii abstract this paper is a continuation of the work in 8 where the authors established the global existence of smooth small data solutions to the general 3 d quasilinear wave equation i j 0 3 g i j u u i j 2 u 0 when the weak null condition holds in the present paper we show that the smooth small data solutions of equation i j 0 3 g i j u u i j 2 u 0 will blow up in finite time when the weak null condition does not hold and a generic nondegenerate condition on the initial data is satisfied moreover a precise blowup time is completely determined therefore collecting the main results in this paper and 8 we have given a basically complete study on the blowup or global existence of small data solutions to the 3 d quasilinear wave equation i j 0 3 g i j u u i j 2 u 0

formation of singularities in three dimensional compressible fluids presented are several results on the formation of singularities in solutions to the three dimensional euler equations for a polytropic ideal fluid under various assumptions on the initial data in particular it is shown that a localized fluid which is initially compressed and outgoing on average will develop singularities regardless of the size of the initial disturbance

asymptotic behaviour of imperfect viscoelastic beams abstract in this paper the problem of the lateral stability of imperfect viscoelastic beams is analysed the problem is examined by means of the quasi static approach and leads to a system of integro differential equations which can be resolved by a series expansions and the laplace transforms the viscous critical load is defined according to the asymptotic behaviour of the beam and can be evaluated by introducing the assumption of weak fading memory solid material and thermodynamic compatibility the critical load does not depend either on the type or the entity of the imperfections furthermore some characteristic aspects of the problem like the faster progress of the torque moment with respect to the progress of the lateral bending moment are underlined for a three element model it is possible to reach a closed form solution in the case of the poisson ratio constant in time and three element model an interesting analogy with the asymptotic behaviour of the imperfect column is observed

on the spectrum of euler bernoulli beam equation with kelvin voigt damping abstract the spectral property of an euler bernoulli beam equation with clamped boundary conditions and internal kelvin voigt damping is considered the essential spectrum of the system operator is rigorously identified to be an interval on the left real axis under some assumptions on the coefficients it is shown that the essential spectrum contains continuous spectrum only and the point spectrum consists of isolated eigenvalues of finite algebraic multiplicity the asymptotic behavior of eigenvalues is presented

pointwise time asymptotic behavior of solutions to a general class of hyperbolic balance laws abstract in this paper we are interested in a general class of hyperbolic balance laws within the frame work of existence of a convex entropy function that symmetrizes the system in certain sense and the kawashima shizuta condition we study the large time behavior of the solution to the cauchy problem in one space dimension for a solution around a constant equilibrium state we predetermine the asymptotic solution as a superposition of the constant state and diffusion waves along the equilibrium characteristic directions we estimate the remainder in the pointwise sense both in space and in time the decay rates in various directions are optimal which further give the optimal l p rates with 1 p applications to several examples including the kerr debye model are given

decay rates of solutions of an anisotropic inhomogeneous n dimensional viscoelastic equation with polynomially decaying kernels we consider the anisotropic and inhomogeneous viscoelastic equation and we prove that the first and second order energy decay polynomially as time goes to infinity when the relaxation function also decays polynomially to zero that is if the kernelg ijkl satisfies dot g ijkl leqq c 0 g ijkl 1 frac 1 p and g ijkl g ijkl 1 frac 1 p in l 1 mathbb r for p 2such that 2 m 1 p then the first and second order energy decay as frac 1 1 t q withq 2 m 1

asymptotic stability in linear viscoelasticity with supplies abstract we present some results about the asymptotic behavior of a linear viscoelastic system making use of the approach based on the concept of minimal state this approach allows to obtain results in a larger class of solutions and data with respect to the classical one based on the histories of the deformation gradient recently a lot of attention has been paid to find unified approaches which permit to study the asymptotic behavior with memory kernels presenting a temporal decay of which the exponential and polynomial decays are only special cases here we extend this unified approach to the dynamic problem in presence of supplies by using the minimal state and compare our results with those present in literature

time dependent asymptotic behavior of the solution for wave equations with linear memory abstract in this article we consider the long time behavior of solutions for the wave equation with linear memory within the theory of process on time dependent spaces we investigate the existence of the time dependent attractor by using the operator decomposition technique and compactness of translation theorem and more detailed estimates furthermore the asymptotic structure of time dependent attractor which converges to the attractor of parabolic equation with memory is proved besides we obtain a further regular result about u t

boundary stabilization for a hybrid system of viscoelasticity in this paper we study the boundary feedback stabilization of a hybrid system that is composed of a viscoelastic thin plate with one part of its edge clamped and the remaining free part attached to a viscoelastic rigid body by adopting the frequency domain method we prove that the boundary feedback controls together with the dissipation induced by the memory effect are strong enough to secure the result of the exponential stability of energy we also reach the result of the exponential stability of the hybrid system on the domain with corners without any extra hypotheses on the regularity of solutions

convergence to diffusion waves of solutions to nonlinear viscoelastic model with fading memory we study the large time behavior inl2 of solutions to a model for the motion of an unbounded homogeneous viscoelastic bar with fading memory decay rates for the solutions are obtained under the assumption that the initial data and histories are smooth and small moreover convergence of the solutions to diffusion waves which are solutions of burgers equations is proved and rates are obtained our method is based on the study of properties of the solutions to the linearized system in the fourier space

numerical solutions to one dimensional problems of thermoelastic contact abstract a numerical method based on the crank nicolson discretisation is applied to one dimensional thermoelastic contact problems such problems can be reduced using an appropriate transformation to the heat equation with a nonlinear and nonlocal source term it is proved that the method converges a number of numerical experiments are presented to illustrate the method and the behavior of the solutions to the problem

global attractors for a semilinear hyperbolic equation in viscoelasticity a semilinear partial differential equation of hyperbolic type with a convolution term describing simple viscoelastic materials with fading memory is considered regarding the past history memory of the displacement as a new variable the equation is transformed into a dynamical system in a suitable hilbert space the dissipation is extremely weak and it is all contained in the memory term longtime behavior of solutions is analyzed in particular in the autonomous case the existence of a global attractor for solutions is achieved

learning regular sets from queries and counterexamples the problem of identifying an unknown regular set from examples of its members and nonmembers is addressed it is assumed that the regular set is presented by a minimamy adequate teacher which can answer membership queries about the set and can also test a conjecture and indicate whether it is equal to the unknown set and provide a counterexample if not a counterexample is a string in the symmetric difference of the correct set and the conjectured set a learning algorithm l is described that correctly learns any regular set from any minimally adequate teacher in time polynomial in the number of states of the minimum dfa for the set and the maximum length of any counterexample provided by the teacher it is shown that in a stochastic setting the ability of the teacher to test conjectures may be replaced by a random sampling oracle ex a polynomial time learning algorithm is shown for a particular problem of context free language identification

local analyticity in weighted spaces and applications to stability problems for volterra equations we study the qualitative properties of the solutions of linear convolution equations such as x x t f x a x f and x t f we are especially concerned with finding conditions which ensure that these equations have resolvents which belong to or are determined up to a term belonging to certain weighted l1 spaces our results are obtained as consequences of more general banach algebra results on functions that are locally analytic with respect to the elements of a weighted l1 space in particular we derive a proposition of wiener levy type for weighted l1 spaces which underlies all subsequent results our method applies equally well to equations more general than those mentioned above we unify and sharpen the results of several recent papers on the asymptotic behavior of volterra convolution equations of the types mentioned above and indicate how many of them can be extended to the fredholm case in addition we give necessary and sufficient conditions on the perturbation term f for the existence of bounded or integrable solutions x in some critical cases when the corresponding limit equations have nontrivial solutions

blowup of the solutions for the ibvp of the isentropic euler equations with damping abstract we establish several results about the blowup of the solutions for the initial boundary value problem of the isentropic euler equations with damping for a gas outside a ball under some assumptions on weighed functionals associated with the initial momentum that they are large enough to develop singularities

existence and decay to contact problems for thermoviscoelastic plates we consider the dynamic contact problem for thermoviscoelastic plates we show the existence of weak solutions as well as exponential decay of the solution

asymptotic behavior of the energy for a class of weakly dissipative second order systems with memory a class of second order abstract systems with memory and dirichlet boundary conditions is investigated by suitable liapunov functionals existence of solutions as well as asymptotic behavior are determined in particular when the memory kernel decays exponentially the polynomially decay of the solutions is proved

global solutions of quasilinear wave equations we show global small data existence for a class of quasilinear wave equations related to einstein s equations in harmonic coordinates these equations do not satisfy the classical null condition and the asymptotic behavior of solutions is not free but the light cones bend at infinity

on the asymptotic behavior of solution for the generalized ibq equation with hydrodynamical damped term abstract we study the cauchy problem for the generalized ibq equation with hydrodynamical damped term in n dimensional space we observe that the dissipative structure of the linearized equation is of the regularity loss type this means that we have the optimal decay estimates of solutions under the additional regularity assumption on the initial data under smallness condition on the initial data we prove the global existence and decay of the small amplitude solution in the sobolev space

global existence and asymptotic behavior for a fractional differential equation this paper is concerned with the global existence and asymptotic behavior of solutions to an initial boundary value problem of hyperbolic type we investigate the interaction between a polynomial source and a dissipation of fractional order this fractional dissipation is defined by a temporal nonlocal term

asymptotic behavior for second order stochastic evolution equations with memory abstract in this paper a general second order integro differential evolution equation with memory driven by multiplicative noise is considered we prove the existence of global mild solution and asymptotic stability of the zero solution using lyapunov function techniques moreover we discuss three examples to show that the asymptotic stability results can be applied to various partial differential equations

boundary controllability and observability of a viscoelastic string in this paper we consider an integrodifferential system which governs the vibration of a viscoelastic one dimensional object we assume that we can act on the system at the boundary and we prove that it is possible to control both the position and the velocity at every point of the body and at a certain time t large enough we shall prove this result using moment theory and we shall prove that the solution of this problem leads to identification of a riesz sequence which solves controllability and observability the results presented here are constructive and can lead to simple numerical algorithms