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 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 …

We analyze the differential system {ρ 1 φ tt− κ (φ x+ ψ) x= 0 ρ 2 ψ tt− b ψ x x+ κ (φ x+ ψ)+ δ θ
x= 0 ρ 3 θ t− 1 β∫ 0∞ g (s) θ xx (t− s) d s+ δ ψ tx= 0 describing a Timoshenko beam coupled …

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 …

In this work we study certain invariant measures that can be associated to the time averaged
observation of a broad class of dissipative semigroups via the notion of a generalized …

In this article, we, first, consider a vibrating system of Timoshenko type in a one-dimensional
bounded domain with an infinite history acting in the equation of the rotation angle. We …

This paper is concerned with existence and uniform (exponential) stability results for a
Moore–Gibson–Thompson equation with memory recently introduced by Lasiecka and …

This paper is concerned with the long-time dynamics of a semilinear wave equation with
degenerate viscoelasticity utt− Δ u+∫ 0∞ g (s) div [a (x)∇ u (t− s)] d s+ f (u)= h (x), defined …