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 …

In this paper, we consider a thermoelastic model where heat conduction is described by the
history dependent version of the Moore–Gibson–Thompson equation, arising via the …

An abstract version of the fourth-order equation∂ ttttu+ α∂ tttu+ β∂ ttu− γ∆∂ ttu− δ∆∂ tu−
ϱ∆ u= 0 subject to the homogeneous Dirichlet boundary condition is analyzed. Such a …

We consider a linear Volterra integro-differential equation of hyperbolic type, which can be
viewed as an abstract version of the equation ∂ _ tt u (t)-\varDelta u (t)+\displaystyle ∫\limits …

We consider the nonclassical diffusion equation with hereditary memory u< sub> t− Δu<
sub> t−∫< sup>∞< sub> 0 κ (s) Δu (t− s) ds+ f (u)= g on a bounded three-dimensional …

We investigate both the mathematical modeling and stability methods for a new integro-
differential system referred to as the viscoelastic Timoshenko–Boltzmann model. The …

We establish an existence, uniqueness and continuous dependence result for the weak
solutions to the nonlinear viscoelastic equation with hereditary memory on a bounded three …

This paper is concerned with a system of nonlinear wave equations with supercritical interior
and boundary sources and subject to interior and boundary damping terms. It is well-known …

We consider the MGT equation with memory $$\partial_ {ttt} u+\alpha\partial_ {tt} u-
\beta\Delta\partial_ {t} u-\gamma\Delta u+\int_ {0}^{t} g (s)\Delta u (ts) ds= 0. $$ We prove an …

In this paper, we consider a Timoshenko system supplemented by a heat equation with a
viscoelastic damping term. We prove an exponential decay of solutions under weak …