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arXiv · 2510.17229

Blow-up rate for the subcritical semilinear heat equation in non-convex domains

Hideyuki Miura·Jin Takahashi·Erbol Zhanpeisov
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Abstract

We consider the semilinear heat equation $u_t=\Delta u+|u|^{p-1} u$ in possibly non-convex and unbounded domains. Our main result shows the nonexistence of type II blow-up for possibly sign-changing solutions in the energy subcritical range $(n-2)p<n+2$. This resolves a long-standing open question dating back to the 1980s and also deduces the blow-up of the scaling critical norm.

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Hideyuki Miura, Jin Takahashi, Erbol Zhanpeisov. 2025-10-20. Blow-up rate for the subcritical semilinear heat equation in non-convex domains. https://arxiv.org/abs/2510.17229

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