Related papers: Energy decay for semilinear evolution equations wi…

In this paper, we obtain some stability results of (abstract) dissipative evolution equations with a nonautonomous and nonlinear damping using the exponential stability of the retrograde problem with a linear and autonomous feedback and a…

We study the large time behavior of solutions to the semilinear wave equation with space-dependent damping and absorbing nonlinearity in the whole space or exterior domains. Our result shows how the amplitude of the damping coefficient, the…

We give an approach to exponential stability within the framework of evolutionary equations due to [R. Picard. A structural observation for linear material laws in classical mathematical physics. Math. Methods Appl. Sci.,…

In this paper we consider second order evolution equations with bounded damping. We give a characterization of a non uniform decay for the damped problem using a kind of observability estimate for the associated undamped problem.

Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving…

In this paper, we consider the Cauchy problem for semilinear $\sigma$-evolution models with an exponential decay memory term. Concerning the corresponding linear Cauchy problem, we derive some regularity-loss-type estimates of solutions and…

In this work, we consider the existence of global solution and the exponential decay of a nonlinear porous elastic system with time delay. The nonlinear term as well as the delay acting in the equation of the volume fraction. In order to…

Exponential stability of the second order linear delay differential equation in $x$ and $u$-control $$ \ddot{x}(t)+a_1(t)\dot{x}(h_1(t))+a_2(t)x(h_2(t))+a_3(t)u(h_3(t))=0 $$ is studied, where indirect feedback control…

We derive sufficient conditions for exponential decay of solutions of the delay negative feedback equation with distributed delay. The conditions are written in terms of exponential moments of the distribution. Our method only uses…

We consider semilinear wave equations with small initial data in two space dimensions. For a class of wave equations with cubic nonlinearity, we show the global existence of small amplitude solutions, and give an asymptotic description of…

This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…

We consider a class of abstract second order evolution equations with a restoring force that is strictly superlinear at infinity with respect to the position, and a dissipation mechanism that is strictly superlinear at infinity with respect…

This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Introducing an appropriate Lyaponuv function, we prove that when the damping is linear, we can find initial…

We consider the global Cauchy problem for a two-component system of cubic semilinear wave equations in two space dimensions. We give a criterion for large time non-decay of the energy for small amplitude solutions in terms of the radiation…

In this paper, we study the Cauchy problem to the linear damped $\sigma$-evolution equation with time-dependent damping in the effective cases \begin{equation*} u_{t t}+(-\Delta)^\sigma u+b(t)(-\Delta)^\delta u_t=0, \end{equation*} and…

We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…

In this paper we analyze a nonlinear abstract evolution equation with an infinite number of time-dependent time delays and a Lipschitz continuous nonlinear term. By using a fixed point argument we prove the existence of a mild solution.…

We consider a second order equation with a linear "elastic" part and a nonlinear damping term depending on a power of the norm of the velocity. We investigate the asymptotic behavior of solutions, after rescaling them suitably in order to…

The exponential stability, in both mean square and almost sure senses, for energy solutions to a class of nonlinear and non-autonomous stochastic PDEs with finite memory is investigated. Various criteria for stability are obtained. An…

This article is devoted to the study of null controllability for evolution equations that incorporate both memory and delay effects. The problem is particularly challenging due to the presence of memory integrals and delayed states, which…