Related papers: Energy decay for evolution equations with glassy t…
In this paper, we study well-posedness and exponential stability for semilinear second order evolution equations with memory and time-varying delay feedback. The time delay function is assumed to be continuous and bounded. Under a suitable…
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…
We study abstract linear and nonlinear evolutionary systems with single or multiple delay feedbacks, illustrated by several concrete examples. In particular, we assume that the operator associated with the undelayed part of the system…
In this paper, we consider a nonlinear Love-equation with infinite memory. By certain properties of convex functions, we use an appropriate Lyapunov functional to find a very general rate of decay for energy (2.3).
We consider an evolution equation whose time-diffusion is of fractional type and we provide decay estimates in time for the $L^s$-norm of the solutions in a bounded domain. The spatial operator that we take into account is very general and…
In this paper, we consider energy decay estimates for the following nonlinear evolution problem $$\begin{split} [P(u_t(t))]_t + A u(t) + B(t , x , u_t(t)) =0,\quad t\in J=(0,\infty), \end{split}$$ under suitable assumptions on the…
We report a molecular dynamics simulation study of the properties of the potential energy landscape sampled by a system of water molecules during the process of generating a glass by cooling, and during the process of regenerating the…
We study a temporally third order (Moore-Gibson-Thompson) equation with a memory term. Previously it is known that, in non-critical regime, the global solutions exist and the energy functionals decay to zero. More precisely, it is known…
In this paper we consider energy decay estimates for the Cauchy problems of dissipative wave equations with time dependent coefficients, in particular, the coefficients consisting of weak dissipation and very fast oscillating terms. For…
We consider the problems of the numerical solution of the Cauchy problem for an evolutionary equation with memory when the kernel of the integral term is a difference one. The computational implementation is associated with the need to work…
We investigate the effect of memory terms on the entropy decay of the solutions to equations with Ornstein-Uhlenbeck operators. Our assumptions on the memory kernels include Caputo-Fabrizio operators and, more generally, the stretched…
The celebrated Mackey-Glass model describes the dynamics of physiological \textit{delayed} systems in which the actual evolution depends on the values of the variables at some \textit{previous} times. This kind of systems are usually…
In this paper, the initial-boundary value problems for the time-fractional degenerate evolution equations are considered. Firstly, in the linear case, we obtain the optimal rates of decay estimates of the solutions. The decay estimates are…
The decay properties of the one-particle Green function in real space and imaginary time are systematically studied for solids. I present an analytic solution for the homogeneous electron gas at finite and at zero temperature as well as…
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.
We study the rate of convergence to equilibrium of the solutions to Fokker-Planck type equations with linear drift by means of Cram\'er and Energy distances, which have been recently widely used in problems related to AI, in particular for…
In this note we study the dynamics of a model recently introduced by one of us, that displays glassy phenomena in absence of energy barriers. Using an adiabatic hypothesis we derive an equation for the evolution of the energy as a function…
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…
We are interested in the Moore-Gibson-Thompson(MGT) equation with memory \begin{equation}\nonumber \tau u_{ttt}+ \alpha u_{tt}+c^2\A u+b\A u_t -\int_0^tg(t-s)\A w(s)ds=0. \end{equation} We first classify the memory into three types. Then we…
This paper is concerned with the energy decay of a viscoelastic variable coefficient wave equation with nonlocality in time as well as nonlinear damping and polynomial nonlinear terms. Using the Lyapunov method, we establish a polynomial…