Stability of an abstract system with infinite history

TL;DR

This paper investigates the stabilization of an abstract linear integrodifferential equation with infinite memory, providing improved conditions for stability in the context of linear viscoelasticity.

Contribution

It introduces new stability results for systems with infinite memory, extending previous findings by relaxing certain conditions on the relaxation function.

Findings

Established stability under less restrictive conditions on the relaxation function

Extended previous results in the literature on viscoelastic systems

Demonstrated the effectiveness of the new stability criteria

Abstract

This work is concerned with stabilization of an abstract linear dissipative integrodiffrential equation with infinite memory modeling linear viscoelasticity where the relaxation function satisfies $ g'(t)\leq -\xi(t)g^p(t), \forall t\geq 0, 1\leq p<\frac{3}{2}$. Our result improves earlier results in the literature.