Long-term behavior for wave equation with nonlinear damping and super-cubic nonlinearity

TL;DR

This paper investigates the long-term dynamics of a semilinear wave equation with nonlinear damping and super-cubic nonlinearity, establishing well-posedness and the existence of global and exponential attractors.

Contribution

It extends the analysis of wave equations by considering broader ranges of nonlinear damping and nonlinearity exponents, proving well-posedness and attractor existence.

Findings

Well-posedness for wider exponent ranges

Existence of global attractor

Existence of exponential attractor

Abstract

In this paper, we consider the semilinear wave equation involving the nonlinear damping term $g(u_t) $ and nonlinearity $f(u)$. The well-posedness of the weak solution satisfying some additional regularity is achieved under the wider ranges of the exponents $g$ and $f$. Moreover, the existence of global attractor and exponential attractor are proved.