Stabilization for the wave equation with fully subciritical logarithmic nonlinearity

Tae Gab Ha

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arXiv · 2603.13179

Stabilization for the wave equation with fully subciritical logarithmic nonlinearity

Tae Gab Ha

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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 $\frac{2(n-1)}{n-2} \leq \gamma < \frac{2n}{n-2}$.

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Tae Gab Ha. 2026-03-13. Stabilization for the wave equation with fully subciritical logarithmic nonlinearity. https://arxiv.org/abs/2603.13179

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