long time behavior of a model of extensible beams with nonlinear boundary dissipations abstract this paper is concerned with the long time behavior of a model of extensible beams u t t u x x x x m 0 l u x 2 d x u x x h defined in a bounded interval 0 l where m is a continuous nonnegative function and h is a static load to this problem little is known with nonlinear boundary conditions one considers the case where a nonlinear forcing interacts with the shear force at the boundary then the existence of a global attractor is proved with a sole boundary damping

stabilization by means of state space depending switching rules abstract in this paper we consider switched systems defined by a pair of linear systems x a 1 x x a 2 x such that there exists a neutrally stable linear combination of the matrices a 1 a 2 under an additional assumption we prove that there exists a state space depending switching rule which stabilizes the system in a very general sense the result is illustrated by some simulations and examples

brief paper global stabilization of semilinear systems using switching controls this paper considers feedback stabilization of distributed semilinear systems using switching controls the semilinear processes together with the switched controllers constitute a type of switched nonlinear system three kinds of stabilizabilities namely weak strong and exponential stabilizabilities are investigated one by one sets of sufficient conditions are obtained for each case a necessary condition for strong stabilizability is given the stabilizing control is characterized using a minimization problem applications to parabolic and hyperbolic like equations are considered

global attractor for the kirchhoff type equation with a strong dissipation abstract the paper studies the longtime behavior of the kirchhoff type equation with a strong dissipation u t t m u 2 u u t h u t g u f x it proves that the related continuous semigroup s t possesses in the phase space with low regularity a global attractor which is connected and an example is shown

global attractors for the extensible thermoelastic beam system abstract this work is focused on the dissipative system t t u x x x x u x x x u l 2 0 1 2 x x u f t x x x x t u g describing the dynamics of an extensible thermoelastic beam where the dissipation is entirely contributed by the second equation ruling the evolution of under natural boundary conditions we prove the existence of bounded absorbing sets when the external sources f and g are time independent the related semigroup of solutions is shown to possess the global attractor of optimal regularity for all parameters r the same result holds true when the first equation is replaced by t t u x x t t u x x x x u x x x u l 2 0 1 2 x x u f with 0 in both cases the solutions on the attractor are strong solutions

kernel sections and uniform attractors of multi valued semiprocesses abstract we present the existence of kernel sections which are all compact invariant and pullback attracting of an infinite dimensional general multi valued process constructed by the set valued backward extension of multi valued semiprocesses moreover the structure of the uniform attractors of a family of multi valued semiprocesses and the uniform forward attraction of kernel sections of a family of general multi valued processes are investigated finally we explain our abstract results by considering the mixed wave systems with supercritical exponent and ordinary differential equations

global attractors for the wave equation with nonlinear damping based on a new a priori estimate method so called asymptotic a priori estimate the existence of a global attractor is proved for the wave equation utt kg ut u f u 0 on a bounded domain r3 with dirichlet boundary conditions the nonlinear damping term g is supposed to satisfy the growth condition c1 s c2 g s c3 1 s p where 1 p 0 is arbitrary the nonlinear term f is supposed to satisfy the growth condition f s c4 1 s q where q 2 it is remarkable that when 2 p 5 we positively answer an open problem in chueshov and lasiecka i chueshov i lasiecka long time behavior of second evolution equations with nonlinear damping math scuola norm sup 2004 and improve the corresponding results in feireisl e feireisl global attractors for damped wave equations with supercritical exponent j differential equations 116 1995 431 447

stabilizing controllers for bilinear systems the problem of finding stabilizing feedback controllers for continuous bilinear systems where the controls act additively and multiplicatively simultaneously is treated the applicability of the quadratic control law of jacobson 5 and others is extended to the case when the a matrix has arbitary eigenvalues under certain conditions a class of bilinear systems common among biochemical flow systems is defined the dyadic bilinear systems a control scheme the so called division controller for dyadic bilinear systems is suggested the practicality of the control schemes is demonstrated on the problem of controlling the neutron level in a fission reactor

undamped nonlinear beam excited by additive l2 regular noise abstract stability of a nonlinear elastic beam excited by a space time dependent nonrandom force or a l 2 regular random noise f x t white in time with general spatial covariance is considered it is supposed that the transversal displacement y of the beam with length l is governed by the quasilinear partial differential equation pde 0 h y t t d y x x x x n 0 e 0 l y x 2 d x y x x k y f x t 0 x l t 0 as a main result we show that its expected energy is linearly bounded at time t in spite of the presence of additive l 2 regular space time noise and cubic type nonlinearities appropriate partial implicit discretization with similar qualitative behavior consistency and stability are discussed as well the technique of lyapunov type functionals processing the information on the related energy e is exploited we compare our results to those for the linear beam in both cases the expected energy e e t is nondecreasing and growing linearly in time t in fact for all nonrandom t s and additive l 2 regular noise f with covariance operator q f with finite trace it satisfies the trace formula e e t e e s trace q f t s 2

unconstrained and constrained stabilisation of bilinear discrete time systems using polyhedral lyapunov functions the constrained and unconstrained stabilisation problem of discrete time bilinear systems is investigated using polyhedral lyapunov functions conditions for a polyhedral set to be both positively invariant and domain of attraction for systems with second order polynomial nonlinearities are first established then systematic methods for the determination of stabilising linear feedback for both constrained and unconstrained bilinear systems are presented attention is drawn to the case where no linear control law rendering the pre specified desired domain of attraction positively invariant exists for this case an approach guaranteeing the existence of a possibly suboptimal solution is established

hecke theory of series formed with modular symbols and relations among convolution l functions in g1 g2 the distribution of modular symbols is studied and a new class of functions which satisfy a transformation law involving these objects is introduced the goal of goldfeld s program is to prove szpiro s conjecture which states that for elliptic curves with minimal discriminant d and conductor n there is an absolute constant such that d n to do this an equivalent conjecture involving modular symbols is established in g4 using the now proven conjecture of shimura taniyama and weil it seems that a sufficiently good understanding of the new series proposed by goldfeld should yield a resolution of these conjectures we repeat here their definition in a somewhat more general form to include period polynomials rather than modular symbols only for positive integers m n such that m n let m k be non negative integers such that m k 2 0 and let be a dirichlet character modulo n first for each f sk m holomorphic cusp forms of weight k and level m we denote by rf the map which sends 0 m the hecke congruence group of level m to the polynomial function

exponential stability of nondissipative linear system in banach space and application to unbounded bilinear systems abstract we consider linear control systems of the form d z t d t a z t b z t where is a real parameter a is the infinitesimal generator of a linear c 0 semigroup of contractions s 0 t on a banach space x and the linear perturbation b is a relatively bounded operator with respect to a we provide necessary and sufficient conditions for exponential stability of the above system our stability results are then applied to establish uniform exponential stabilization of linear and bilinear systems with unbounded control operators applications to hyperbolic like equations are considered

attractors for processes on time dependent spaces applications to wave equations abstract for a process u t x x t acting on a one parameter family of normed spaces we present a notion of time dependent attractor based only on the minimality with respect to the pullback attraction property such an attractor is shown to be invariant whenever u t is t closed for some t 0 a much weaker property than continuity defined in the text as a byproduct we generalize the recent theory of attractors in time dependent spaces developed in di plinio et al 2011 13 finally we exploit the new framework to study the longterm behavior of wave equations with time dependent speed of propagation

global attractors for wave equations with nonlinear interior damping and critical exponents abstract in this paper we study the global attractors for wave equations with nonlinear interior damping we prove the existence regularity and finite dimensionality of the global attractors without assuming a large value for the damping parameter when the growth of the nonlinear terms is critical

remark on the decay for damped string and beam equations where a is an operator in a hilbert space h m is a real function our results improve those obtained by de brito in a recent paper l we briefly recall the notation and the assumptions in l referring to this paper for other information on physical meaning existence and regularity theory applications and bibliography let a be a self adjoint positive operator in a real hilbert space h with dense domain v we assume that 5 0 is the least eigenvalue of a so a u au u 3 51 1 for u e v let m e cl be a real nondecreasing function such that m s 2 p ks k z 0 p real we have with the notation

stochastic euler bernoulli beam driven by additive white noise global random attractors and global dynamics abstract this paper concerns with the long time dynamical behavior of a stochastic euler bernoulli beam driven by additive white noise by verifying the existence of absorbing set and obtaining the stabilization estimation of the dynamical system induced by the beam the existence of global random attractors that attracts all bounded sets in phase space is proved furthermore the finite hausdorff dimension for the global random attractors is attained in light of the relationship between global random attractor and random invariant probability measure the global dynamics of the beam are analyzed according to numerical simulation on global random basic attractors and global random point attractors

dynamics of a class of odes more general than almost periodic abstract a temporally global solution if it exists of a nonautonomous ordinary differential equation need not be periodic almost periodic or almost automorphic when the forcing term is periodic almost periodic or almost automorphic respectively an alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here specifically the class of functions consists of uniformly continuous functions defined on the real line and taking values in a banach space which have pre compact ranges besides periodic and almost periodic functions this class also includes many nonrecurrent functions assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts the existence of a special bounded entire solution as well the existence of stable and unstable manifolds of this solution are established moreover it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation in the stable case it is shown that this special solution is the pullback attractor of the system a class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a c 0 semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations

local and global wellposedness of weak solutions for the wave equation with nonlinear boundary and interior sources of supercritical exponents and damping abstract we consider the wave equation with interior and boundary nonlinear sources and damping and we are interested in local and global wellposedness of finite energy solutions the main difficulty is represented by the fact that the lopatinski condition fails to hold unless the dim 1 and thus the analysis of the boundary nonlinearities becomes a subtle issue

stabilizability of second order bilinear systems this note states necessary and sufficient conditions for the existence of a linear state feedback controller such that a second order bilinear system has a globally asymptotically stable closed loop a suitable controller is constructed for each system which satisfies the conditions

a concept of energy banach space and its application to the gradient method the notion of energy banach space is introduced for nonlinear operators and some properties are discussed the concept is used to extend the gradient method for operators which are not continuous themselves but their transform to a suitable energy space has appropriate continuity and monotonicity properties convergence is obtained in the energy norm the obtained method is applied to quasilinear elliptic boundary value problems

finite dimensional attractors for the kirchhoff models the paper studies the existence of the finite dimensional global attractor and exponential attractor for the dynamical system associated with the kirchhoff models arising in elasto plastic flow utt div u m 1 u ut 2u h ut g u f x by using the method of l trajectories and the operator technique it proves that under subcritical case 1 m n 2 n 2 the above mentioned dynamical system possesses in different phase spaces a finite dimensional weak global attractor and a weak exponential attractor respectively for application the fact shows that for the concerned elasto plastic flow the permanent regime global attractor can be observed when the excitation starts from any bounded set in phase space and the fractal dimension of the attractor that is the number of degree of freedom of the turbulent phenomenon and thus the level of complexity concerning the flow is finite

stability improvement of nonlinear systems by feedback this paper is concerned with the property of stabilizing a nonlinear system to a specified equilibrium point arbitrarily fast by appropriate smooth feedback two closely related forms of this property are explored one refers to the asymptotic transfer to the critical point with exponential decay and it is shown that the systems possessing the above property are precisely those whose corresponding linearization is controllable the second stabilizability form defined here amounts to driving the system back to an arbitrarily small neighborhood of the given point arbitrarily fast by smooth feedback a global stabilization result is also included finding application in hamiltonian systems special emphasis is given to the bilinear case

finite dimensionality and regularity of attractors for a 2 d semilinear wave equation with nonlinear dissipation we consider a semilinear wave equation defined on a two dimensional bounded domain with a nonlinear dissipation our main result is that the flow generated by the model is attracted by a finite dimensional global attractor in addition this attractor has additional regularity properties that depend on regularity properties of nonlinear functions in the equation to our knowledge this is a first result of this type in the context of higher dimensional wave equations

positive solutions for a quasilinear elliptic equation of kirchhoff type this paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the type m w u 2dx du f x u email protected u 0 email protected email protected where w is a smooth bounded domain of n m is a positive function and f has subcritical growth

global solutions to a structure acoustic interaction model with nonlinear sources abstract this article focuses on a structural acoustic interaction system consisting of a semilinear wave equation defined on a smooth bounded domain r 3 which is strongly coupled with a berger plate equation acting only on a flat part of the boundary of in particular the source terms acting on the wave and plate equations are allowed to have arbitrary growth order we employ a standard galerkin approximation scheme to establish a rigorous proof of the existence of local weak solutions in addition under some conditions on the parameters in the system we prove such solutions exist globally in time and depend continuously on the initial data

on an extensible beam equation with nonlinear damping and source terms the paper studies the global existence stability and the longtime dynamics of solutions to the initial boundary value problem ibvp of an extensible beam equation with nonlinear damping and source terms utt m u 2 u 2u g ut f u h it proves that i the ibvp is global well posed provided that either the growth exponent p of the source term f u is non supercritical that is 2 p p n 4 n 4 and p q if n 5 or p is supercritical but is dominated by the growth exponent q of the nonlinear damping g ut i e p p if n 5 iii especially when the space dimension n 4 all the above mentioned conclusions hold without any restriction on p and q that is 1 p q

energy methods for quasilinear hyperbolic initial boundary value problems applications to elastodynamics the aim of this paper is to show how energy methods can be used to establish local in time existence of smooth solutions to certain initial boundary value problems for systems of quasilinear hyperbolic partial differential equations our particular objective is to treat the equations of nonlinear elastodynamics

global solution and regularizing properties on a class of nonlinear evolution equation abstract in this paper we will consider the equation formula where formula the initial value problem is proved to be locally well posed for initial data taken ind a2 d a3 2 and globally well posed for small data in this case we also show the exponential decay of the solution as time goes to infinity the main result of this paper is to prove that the solution has the smooting effect property on the initial data this means that if the initial data belongs tod a2 d a3 2 then the solutionubelongs toc 0 d ak k n providedm n andrarec function

global and exponential attractors for extensible thermoelastic plate with time varying delay abstract a class of nonlinear problems modeling thermoelastic extensible plates with rotational inertia and time dependent delay in the internal feedback are considered by virtue of galerkin method combined with the priori estimates we prove the existence and uniqueness of global solution the proof with or without rotational inertia does not depend on the parameters 1 and 2 of time dependent delay moreover the existence of compact global and exponential attractors is proved through a stabilizability estimate this estimate which is established under restrictions on 1 and 2 and independently of the rotational inertia parameter provides bounds on the attractors fractal dimension other property such as additional smoothness of global attractors with respect to parameter is also presented furthermore the existence of a generalized fractal exponential attractor is also derived finally we show that the family of global attractors is continuous with respect to the parameter in some sense

asymptotic stabilization of the bilinear time invariant system via piecewise constant feedback abstract sufficient conditions for the asymptotic stabilization in a preassigned domain of the nonhomogeneous bilinear system bls via piecewise constant feedback are given based on those for an auxillary bls with additional control in the drift term application to the swing equation is also discussed

global attractors and their hausdorff dimensions for a class of kirchhoff models this paper studies the existence regularity and hausdorff dimensions of global attractors for a class of kirchhoff models arising in elastoplastic flow utt div u m 1 u ut 2u h ut g u f x it proves that under rather mild conditions the dynamical system associated with above mentioned models possesses in phase space x a global attractor which has further regularity in x 1 x and has finite hausdorff dimension for application the fact shows that for the concerned elastoplastic flow the permanent regime global attractor can be observed when the excitation starts from any bounded set in phase space and the dimension of the attractor that is the number of degree of freedom of the turbulent phenomenon and thus the level of complexity concerning the flow is finite

time dependent attractor for plate equations on rn abstract we first introduce a new notation so called asymptotic contractive process on the time dependent entire space and then prove that such asymptotic contractive process is pullback asymptotically compact finally we show that the existence of time dependent attractor for the plate equation on h 2 r n l 2 r n by using this new abstract result

on the kirchhoff plates equations with thermal effects and memory boundary conditions in this paper we study the existence of weak and strong global solutions and uniform decay of the energy to the kirchhoff plates equations with thermal effect and memory conditions working at the boundary we show that the dissipation produced by the memory effect not depend on the present values of temperature gradient that is we show that the dissipation produced by memory effect is strong enough to produce exponential decay of the solution provided the relaxation functions also decays exponentially when the relaxation functions decays polynomially we show that the solution decays polynomially with the same rate

remarks on an elliptic equation of kirchhoff type abstract we present a short survey on the nonlocal elliptic boundary value problem m u 2 d x u f x u in u 0 on where is a smooth bounded domain of r n m is a positive function and f has subcritical growth

long time dynamics of von karman semi flows with non linear boundary interior damping abstract we study von karman evolution equations with non linear dissipation and with partially clamped and partially free boundary conditions two distinctive mechanisms of dissipation are considered i internal dissipation generated by non linear operator and ii boundary dissipation generated by shear forces friction acting on a free part of the boundary the main emphasis is given to the effects of boundary dissipation under suitable hypotheses we prove existence of a compact global attractor and finiteness of its fractal dimension we also show that any solution is stabilized to an equilibrium and estimate the rate of the convergence which in turn depends on the behaviour at the origin of the functions describing the dissipation

global attractors for von karman evolutions with a nonlinear boundary dissipation abstract dynamic von karman equations with a nonlinear boundary dissipation are considered questions related to long time behaviour existence and structure of global attractors are studied it is shown that a nonlinear boundary dissipation with a large damping parameter leads to an existence of global compact attractor for all weak finite energy solutions this result has been known in the case of full interior dissipation but it is new in the case when the boundary damping is the main dissipative mechanism in the system in addition we prove that fractal dimension of the attractor is finite the proofs depend critically on the infinite speed of propagation associated with the von karman model considered

decay of energy for second order boundary hemivariational inequalities with coercive damping abstract in this article we consider the asymptotic behavior of solutions to second order evolution inclusions with the boundary multivalued term u t a t u t b u t j t u t 0 and u t a t u t b u t j t u t 0 where a is a possibly nonlinear coercive and pseudomonotone operator b is linear continuous symmetric and coercive is the trace operator and j is a locally lipschitz integral functional with denoting the clarke generalized gradient taken with respect to the second variable for both cases we provide conditions under which the appropriately defined energy decays exponentially to zero as time tends to infinity we discuss assumptions and provide examples of multivalued laws that satisfy them

explosive solutions of stochastic nonlinear beam equations with damping abstract this study considers a class of damped stochastic nonlinear beam equations driven by multiplicative noise by an appropriate energy inequality we provide sufficient conditions such that the local solutions of the stochastic equations blow up with a positive probability or are explosive in an l 2 sense we also derive estimates of the upper bound of the blow up time

uniform attractors for a non autonomous viscoelastic equation with a past history abstract this paper investigates the existence of uniform attractors for a non autonomous viscoelastic equation with a past history in a bounded domain r n n 1 by establishing the uniformly asymptotic compactness of the semi process generated by the global solutions our results improve those results by araujo et al 2013

an attractor for a nonlinear dissipative wave equation of kirchhoff type abstract in this paper we prove the existence and some absorbing properties of an attractor in a local sense for the initial boundary value problem of a quasilinear wave equation of kirchhoff type with a standard dissipation u t

global attractor for plate equation with nonlinear damping abstract in this paper we study the long time behavior of plate equation with nonlinear damping and critical nonlinearity we prove the existence of a global attractor in the space h 0 2 l 2

properties of eisenstein series formed with modular symbols in this work a new kind of non holomorphic eisenstein series first introduced by goldfeld is studied for an arbitrary fuchsian group of the first kind we fix a holomorphic cusp form and consider eisenstein series constructed with the modular symbol associated with this cusp form we develop the theory analogously with that of the usual eisenstein series starting with its meromorphic continuation to the entire complex plane a functional equation is then obtained relating the values at s to those at 1 s introduction let h z c im z 0 be the upper half plane and let sl2 r be a fixed non co compact fuchsian group of the first kind for example n 0 n acting on h for simplicity assume that has a unique cusp at infinity with stability group 1 m 0 1 m z for each in we shall label its matrix elements a b c d let f z be an element of s2 the space holomorphic cusp forms of weight 2 for following go we define a modified eisenstein series 0 1 e z s f im z s z h where for the modular symbol is given by f 2 i w w f d the definition being independent of w h note that since 1 2 f 1 f 2 f the series is not automorphic the transformation rule is e z s e z s f e z s for all where e z s is the usual eisenstein series for this new type of non holomorphic eisenstein series was introduced by goldfeld in order to study the distribution properties of modular symbols f as ranges over the group the series 0 1 converges for re s 2 and goldfeld hypothesised that it should have an analytic continuation and a functional equation in this paper selberg s method described in iw he is extended to establish the following results typeset by ams tex 1

feedback stabilization of discrete time homogeneous semi linear systems for discrete time semi linear systems satisfying an accessibility condition asymptotic null controllability is equivalent to exponential feedback stabilizability using a piecewise constant feedback a constructive procedure that yields such a feedback is presented

dimension of the global attractor for damped semilinear wave equations with critical exponent we obtain an estimate of the upper bound of the hausdorff dimension of the global attractor for damped semilinear wave equations with a critical exponent the obtained hausdorff dimension decreases as the damping grows for large damping

global attractor for a class of kirchhoff models the paper studies the longtime behavior of solutions to the initial boundary value problem ibvp for a class of kirchhoff models arising in elastoplastic flow utt div u m 1 u ut 2u h ut g u f x by combining the decomposition idea with the operate technique it proves that under rather mild conditions the dynamical system associated with above mentioned ibvp possesses in different phase spaces a global attractor which is connected respectively for application the fact shows that for the concerned elastoplastic flow the permanent regime global attractor can be observed when the excitation starts from any bounded set in phase space

global attractors for von karman equations with nonlinear interior dissipation abstract in this paper we study the asymptotic behavior of weak solutions for von karman equations with nonlinear interior dissipation we prove the existence of a global attractor in the space w 2 2 l 2

upper semicontinuity of pullback attractors for a non autonomous viscoelastic equation this paper is concerned with upper semicontinuity of pullback attractors for a non autonomous viscoelastic equation with a past history with a nonautonomous perturbation in particular under some proper assumptions we prove that the pullback attractor a e t t r of eq 1 1 with e 0 and the global attractor a of eq 1 1 with e 0 satisfy lim e 0 dist x a e t a 0 for any email protected r

on controllability of second order nonlinear impulsive differential systems abstract many dynamical systems in physics chemistry biology and engineering sciences have impulsive dynamical behaviors due to abrupt jumps at certain instants during the dynamical processes the mathematical models of such processes are called differential systems with impulse effect this paper studies the exact controllability issue of certain types of second order nonlinear impulsive control differential systems sufficient conditions are formulated and proved for the exact controllability of such systems without imposing a compactness condition on the cosine family of operators we establish controllability results by using a fixed point analysis approach finally an example is presented to illustrate the utility of the proposed result the results improve some recent results

stochastic nonlinear beam equations an extensible beam equation with a stochastic force of a white noise type is studied lyapunov functions techniques being used to prove existence of global mild solutions and asymptotic stability of the zero solution

long time dynamics of an extensible plate equation with thermal memory abstract this work is concerned with long time dynamics of solutions of extensible plate equations with thermal memory the problem corresponds to a model of thermoelasticity based on a theory of non fourier heat flux by considering the case where rotational inertia is present we show that the thermal dissipation is sufficient to stabilize the system and guarantees the existence of a finite dimensional global attractor in addition the existence of exponential attractors is also considered

necessary and sufficient conditions for the existence of time dependent global attractor and application in this paper we are concerned with infinite dimensional dynamical systems in time dependent space first we characterize some necessary and sufficient conditions for the existence of the time dependent global attractor by using a measure of noncompactness then we give a new method to verify the sufficient condition as a simple application we prove the existence of the time dependent global attractor for the damped equation in strong topological space

on the existence of a global attractor for the wave equation with nonlinear strong damping perturbed by nonmonotone term abstract the long time behavior of the wave equation with nonmonotone interior damping is considered it is shown that the semigroup generated by this equation possesses a global attractor in h 0 1 l 2

partial stabilisation of semilinear systems using bounded controls this paper studies a partial stabilisation problem for distributed semilinear systems this consists of steering only a part of the system s state to its equilibrium constrained controls are proposed to force the desired part of the state to approach the equilibrium necessary and sufficient conditions for weak and strong partial stabilisation are given applications are presented

global attractor for a model of extensible beam with nonlinear damping and source terms abstract this paper is concerned with the existence of a global attractor for the nonlinear beam equation with nonlinear damping and source terms u t t 2 u m u 2 d x u f u g u t h in r where is a bounded domain of r n m is a nonnegative real function and h l 2 the nonlinearities f u and g u t are essentially u u u u and u t r u t respectively with r 0 and this kind of problem models vibrations of extensible beams and plates

reachable sets and controllability of bilinear time invariant systems a qualitative approach this paper is concerned with a qualitative method for the study of reachable sets and controllability of bilinear time invariant systems a nonlinear decomposition technique which reduces the solution of the problem to the analysis of the qualitative behavior of a finite number of linear uncontrolled systems is introduced special consideration is given to the homogeneous bilinear systems with commutative matrices two and three dimensional examples are discussed

large deviations for stochastic nonlinear beam equations abstract we establish a large deviation principle for the solutions of stochastic partial differential equations for nonlinear vibration of elastic panels also called stochastic nonlinear beam equations

on a global solution and asymptotic behaviour for the generalized damped extensible beam equation abstract we prove the existence and uniqueness of global solutions for the cauchy problem concerning the evolution equation u a 2 u m a 1 2 u 2 h au g u 0 suggested by the study of plates and beams where a is a linear operator in a hilbert space h and m and g are real functions we also study the asymptotic behaviour of the solutions under suitable growth assumptions on the nonlinear term g

global existence and blow up of solutions for a kirchhoff type plate equation with damping the initial boundary value problem for a kirchhoff type plate equation in a bounded domain is considered we show the blow up of solutions and the lifespan estimates for three different ranges of initial energy global existence of solutions is proved by the potential well theory and decay estimates of the energy function are established by using nakao s inequality

cauchy problem for quasi linear wave equations with viscous damping abstract the paper studies the global existence and asymptotic behavior of weak solutions to the cauchy problem for quasi linear wave equations with viscous damping it proves that when p max m where m 1 1 and p 1 are respectively the growth orders of the nonlinear strain terms the nonlinear damping term and the source term the cauchy problem admits a global weak solution which decays to zero according to the rate of polynomial as t as long as the initial data are taken in a certain potential well and the initial energy satisfies a bounded condition especially in the case of space dimension n 1 the solutions are regularized and so generalized and classical solution both prove to be unique comparison of the results with previous ones shows that there exist clear boundaries similar to thresholds among the growth orders of the nonlinear terms the states of the initial energy and the existence asymptotic behavior and nonexistence of global solutions of the cauchy problem

time dependent global attractor for extensible berger equation abstract in this paper we investigate the asymptotic behavior of the nonautonomous berger equation e t u t t 2 u q u 2 d x u g u t u f t on a bounded smooth domain r n with hinged boundary condition where e t is a decreasing function vanishing at infinity under suitable assumptions we establish an invariant time dependent global attractor within the theory of process on time dependent space

remarks on the beam evolution equations in noncylindrical domains abstract in this article we present results concerning the existence uniqueness and the asymptotic behavior of solutions for a beam evolution equation with variable coefficients in noncylindrical domains

uniform attractor for non autonomous hyperbolic equation with critical exponent abstract in this paper we study the uniform attractor for semilinear wave equation with mixed differential quotient terms and critical nonlinearity we prove the existence of the uniform attractor in h 0 1 l 2

energy decay of a microbeam model with a locally distributed nonlinear feedback control abstract in this paper we address the problem of internal stabilization of the deflection of a microbeam which is modeled by a sixth order hyperbolic equation employing multiplier techniques and an integral inequality we prove that a locally distributed nonlinear feedback control forces the energy associated to the deflection to decay exponentially or polynomially to zero as a consequence of this the deflection goes to the rest position as the time goes to infinity