Global attractors for nonlinear viscoelastic equations with memory

TL;DR

This paper investigates the long-term behavior of solutions to a nonlinear viscoelastic equation with memory, proving the existence of a highly regular global attractor under broad conditions on nonlinearities and memory kernels.

Contribution

It establishes the existence of a global attractor with optimal regularity for a wide class of nonlinear viscoelastic equations with hereditary memory, under general conditions.

Findings

Existence of a global attractor with optimal regularity.

Applicability to a broad class of nonlinearities.

General conditions on the memory kernel are sufficient.

Abstract

We study the asymptotic properties of the semigroup S(t) arising from a nonlinear viscoelastic equation with hereditary memory on a bounded three-dimensional domain written in the past history framework of Dafermos. We establish the existence of the global attractor of optimal regularity for S(t) for a wide class of nonlinearities as well as within the most general condition on the memory kernel.