Stabilization for the wave equation with fully subciritical logarithmic nonlinearity

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 $2<{\hat{I}}^3<\frac{2(n-1)}{n-2}$, we successfully extend the validity of the well-posedness and stabilization results to the upper subcritical range $\frac{2(n-1)}{n-2}\le {\hat{I}}^3<\frac{2n}{n-2}$.