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arXiv · 2406.14218

Stability of nondegenerate ODE type blowup for the Fujita type heat equation

Junichi Harada
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Abstract

The asymptotic bahavior of blowup solutions to the Fujita type heat equation $u_t=\Delta u+|u|^{p-1}u$ is studied. This equation admits the ODE type blowup given by $u(x,t)=(p-1)^\frac{1}{p-1}(T-t)^{-\frac{1}{p-1}}$. It is known that nondegenerate ODE type blowup is stable if $p\in(1,\frac{n+2}{n-2})$ due to Fermanian Kammerer-Merle-Zaag (2000). This paper extends their result to more general case.

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Junichi Harada. 2024-06-20. Stability of nondegenerate ODE type blowup for the Fujita type heat equation. https://arxiv.org/abs/2406.14218

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