Smooth dynamics of a sup-cubic wave equation with delays

Abstract

Abstract We establish the existence of a time-dependent exponential smooth attractor for a weakly damped wave equations with sup-cubic nonlinearity and hereditary effects in a 3D bounded domain. Our methods are mainly based on the recent extension of Strichartz estimates to the case of bounded domains, a more general criterion constructed by the quasi-stable technique and the standard bootstrapping technique.

Keywords

• Wave equation
• Delay
• Shatah–Struwe solution
• Exponential attractor
• Sup-cubic nonlinearity