Uniform attractor and its Kolmogorov entropy for a damped sup-cubic wave equation with state-dependent delay

Abstract

The well-posedness and asymptotic dynamics of non-autonomous wave equations with state-dependent delay and sup-cubic nonlinearity are investigated. Based on the Strichartz estimates, we first obtain the well-posedness in a $ C^1 $-type space. Then, we present a general scheme for considering the dynamics, which generalizes the method of quasi-stability to the non-autonomous setting. Applying this scheme to our concrete model, we establish the existence of a uniform attractor and give its entropy estimates.