指数半线性热方程的熵不稳定性和刚性
Entropy instability and rigidity for the exponential semilinear heat equation
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中文总结 AI 辅助
本文利用$F$-泛函和熵研究指数半线性热方程的有界自相似解，证明非常数解熵不稳定且平凡解定量孤立，给出变分不稳定性和刚性定理。
中文摘要 AI 辅助
本文通过$F$-泛函和熵研究指数半线性热方程的有界自相似解。受平均曲率流最新进展的启发，我们证明了自相似方程的每个非常数有界解都是熵不稳定的。我们还表明平凡轮廓$w\equiv0$在有界解中是定量孤立的。这些结果为非平凡轮廓提供了变分不稳定性定理，并为平凡轮廓提供了刚性定理。
英文摘要
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.
发表机构
- Department of Mathematical Sciences, Tsinghua University（清华大学数学科学系）
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