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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≡0 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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Cite

BibTeXRIS
BibTeX
@misc{guo2026entropy,
  title = {{Entropy instability and rigidity for the exponential semilinear heat equation}},
  author = {Yuxia Guo and Jionghao Lv},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34541},
  eprint = {2609.34541},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34541},
}
RIS
TY  - UNPB
TI  - Entropy instability and rigidity for the exponential semilinear heat equation
AU  - Yuxia Guo
AU  - Jionghao Lv
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.34541
UR  - https://arxiv.org/abs/2609.34541
AB  - 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≡0 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.
ER  -