Stabilization for the wave equation with fully subciritical logarithmic nonlinearity

TL;DR

This paper investigates the stabilization and well-posedness of a wave equation with strong damping and logarithmic nonlinearity, extending results to a broader subcritical range of the nonlinearity parameter.

Contribution

It extends the well-posedness and stabilization results for the wave equation with logarithmic nonlinearity to the upper subcritical range, beyond previous restrictions.

Findings

Established local and global existence of solutions.

Proved uniform energy decay rates.

Extended well-posedness results to a larger parameter range.

Abstract

In this paper, we consider a wave equation with strong damping and logarithmic nonlinearity. This paper aims to study the local and global existence, uniqueness and the uniform energy decay rate of a weak solution under some sufficient conditions on the initial data. Unlike previous literature restricted to the lower subcritical range $2 < \gamma < \frac{2(n-1)}{n-2}$, we successfully extend the validity of the well-posedness and stabilization results to the upper subcritical range $\frac{2(n-1)}{n-2} \leq \gamma < \frac{2n}{n-2}$.