Related papers: Uniform attractors for non-autonomous wave equatio…
The authors consider non-autonomous dynamical behavior of wave-type evolutionary equations with nonlinear damping and critical nonlinearity. These type of waves equations are formulated as non-autonomous dynamical systems (namely,…
We give a comprehensive study of strong uniform attractors of non-autonomous dissipative systems for the case where the external forces are not translation compact. We introduce several new classes of external forces which are not…
In this paper we consider sufficient conditions for the existence of uniform compact global attractor for non-autonomous dynamical systems in special classes of infinite-dimensional phase spaces. The obtained generalizations allow us to…
We study pullback attractors of non-autonomous non-compact dynamical systems generated by differential equations with non-autonomous deterministic as well as stochastic forcing terms. We first introduce the concepts of pullback attractors…
We give a detailed study of attractors for measure driven quintic damped wave equations with periodic boundary conditions. This includes uniform energy-to-Strichartz estimates, the existence of uniform attractors in a weak or strong…
In this paper, we first establish a criterion based on contractive function for the existence of polynomial attractors. This criterion only involves some rather weak compactness associated with the repeated limit inferior and requires no…
The paper investigates the existence and upper semicontinuity of uniform attractors of the perturbed non-autonomous Kirchhoff wave equations with strong damping and supercritical nonlinearity: $u_{tt}-\Delta u_{t}-(1+\epsilon\|\nabla…
In this paper we prove the existence of the global attractor for the wave equation with nonlocal weak damping, nonlocal anti-damping and critical nonlinearity.
We study long-time dynamics of a class of abstract second order in time evolution equations in a Hilbert space with the damping term depending both on displacement and velocity. This damping represents the nonlinear strong dissipation…
The wave equation with energy critical sources and nonlinear damping defined on a 3D bounded domain is considered. It is shown that the resulting dynamical system admits a global attractor. Under the additional assumption of strong…
In this paper, we investigate the dynamical behavior of non-autonomous Lame thermoelastic systems within $N$-dimensional materials. With appropriate constraints on nonlinear characteristics and functional parameters, we initially establish…
The paper gives a detailed study of long-time dynamics generated by weakly damped wave equations in bounded 3D domains where the damping exponent depends explicitly on time and may change sign. It is shown that in the case when the…
We consider a class of wave equations with constant damping and polynomial nonlinearities that are perturbed by small, multiplicative, space-time white noise. The equations are defined on a one-dimensional bounded interval with Dirichlet…
The aim of this paper is to study the robustness of the family of pullback attractors associated to a non-autonomous coupled system of strongly damped wave equations, given by the following evolution system $$\left\{ \begin{array}{lr}…
We establish the well-posedness of a strongly damped semilinear wave equation equipped with nonlinear hyperbolic dynamic boundary conditions. Results are carried out with the presence of a parameter distinguishing whether the underlying…
We study the long-time behavior of solutions of the one dimensional wave equation with nonlinear damping coefficient. We prove that if the damping coefficient function is strictly positive near the origin then this equation possesses a…
This paper is concerned with long-time dynamics of semilinear wave equations defined on bounded domains of $\mathbb{R}^3$ with cubic nonlinear terms and locally distributed damping. The existence of regular finite-dimensional global…
This note is focused on a novel technique in order to establish the boundedness in more regular spaces for global attractors of dissipative dynamical systems, without appealing to uniform-in-time estimates. As an application of the abstract…
The long-term behaviour of solutions to a model for acoustic-structure interactions is addressed; the system is comprised of coupled semilinear wave (3D) and plate equations with nonlinear damping and critical sources. The questions of…
In this work we study nonuniform exponential dichotomies and existence of pullback and forward attractors for evolution processes associated to nonautonomous differential equations. We define a new concept of nonuniform exponential…