Regular global attractors for wave equations with degenerate memory

TL;DR

This paper proves the existence of a regular global attractor for a wave equation with degenerate memory, demonstrating the attractor's compactness and regularity under certain conditions.

Contribution

It establishes the existence and regularity of global attractors for wave equations with degenerate viscoelastic dissipation, extending previous results.

Findings

Existence of a compact absorbing set

Global attractor consists of regular solutions

Enhanced regularity results for the attractor

Abstract

We consider the wave equation with degenerate viscoelastic dissipation recently examined in Cavalcanti, Fatori, and Ma, Attractors for wave equations with degenerate memory, J. Differential Equations (2016). Under some additional assumptions, we show the existence of a compact absorbing set. This result provides further regularity for the global attractor and shows that it consists of regular solutions.