Regular global attractors for wave equations with degenerate memory

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.