In this survey paper, we discuss the decay properties of the semigroup generated by a linear
integro-differential equation in a Hilbert space, which is an abstract version of the equation tt …

We now apply thermodynamic principles to field theories with memory. For general
nonlinear, nonisothermal theories, we assume that a free energy is given, this being the …

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 …

We discuss a novel approach to the mathematical analysis of equations with memory, based
on a new notion of state. This is the initial configuration of the system at time t= 0 which can …

We address the study of the asymptotic behavior of solutions to an abstract
integrodifferential equation modeling linear viscoelasticity. Framing the equation in the past …

This book provides a unified treatment of continuum physics. A systematic approach to the
balance equations is elaborated for wide-ranging classes of materials (classical continua …

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 …

In this paper, we consider a second-order abstract linear equation with infinite memory and
time delay terms. Under appropriate assumptions on the convolution kernel and on the …

This paper is concerned with the following memory-type Timoshenko system ρ 1 φ tt-K (φ x+
ψ) x= 0, ρ 2 ψ tt-b ψ xx+ K (φ x+ ψ)+∫ 0+∞ g (s) ψ xx (ts) ds= 0, with Dirichlet boundary …

This paper is concerned with a class of plate equations with memory in a history space
setting and perturbations of p-Laplacian type u_ tt+ α Δ^ 2u-Δ _pu--∞^ t μ (ts) Δ^ 2u (s) ds-Δ …