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arXiv · 2505.12264

Liouville theorem for subcritical nonlinear heat equation

Yang Zhou
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Abstract

We obtain a Li-Yau-type estimate for nonnegative ancient solutions to the subcritical semilinear heat equation $\frac{\p u}{\p t}=\De u+u^p$ in $\rz^n\times(-\infty,0)$. Then, we combine the Li-Yau type estimate and Melre-Zaag's result to prove the Liouville theorem of this equation.

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Yang Zhou. 2025-05-18. Liouville theorem for subcritical nonlinear heat equation. https://arxiv.org/abs/2505.12264

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