Strongly damped wave equation with exponential nonlinearities

TL;DR

This paper investigates the well-posedness and long-term behavior of a 2D strongly damped wave equation with exponential nonlinearities, establishing existence of solutions and a global attractor.

Contribution

It introduces new results on the existence and global attractor for a damped wave equation with exponential source and damping terms.

Findings

Proved well-posedness of the problem

Established existence of a global attractor

Analyzed the long-term dynamics of the system

Abstract

In this paper, we study the initial boundary value problem for the two dimensional strong damped wave equation with exponentially growing source and damping terms. We first show the well-posedness of this problem and then prove the existence of the global attractor in $(H_{0}^{1}(\Omega)\cap L^{\infty}(\Omega))\times L^{2}(\Omega)$.