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arXiv · 2609.34541

Entropy instability and rigidity for the exponential semilinear heat equation

Yuxia Guo·Jionghao Lv
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Abstract

In this paper, we study bounded self-similar solutions for the exponential semilinear heat equation via the $F$-functional and entropy. Motivated by recent developments in mean curvature flow, we prove that every non-constant bounded solution of the self-similar equation is entropy unstable. We also show that the trivial profile $w\equiv0$ is quantitatively isolated among bounded solutions. These results provide both a variational instability theorem for nontrivial profiles and a rigidity theorem for the trivial profile.

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Yuxia Guo, Jionghao Lv. 2026-09-28. Entropy instability and rigidity for the exponential semilinear heat equation. https://arxiv.org/abs/2609.34541

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