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arXiv · 2504.15639

A remark for characterizing blowup introduced by Giga and Kohn

Wangzhe Wu
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Abstract

Giga and Kohn studied the blowup solutions for the equation $v_{t} - \Delta v - |v|^{p - 1} v = 0 $ and characterized the asymptotic behavior of $v$ near a singularity. In the proof, they reduced the problem to a Liouville theorem for the equation $\Delta u - \frac{1}{2} x \cdot \nabla u + |u|^{p - 1} u - \beta u = 0$ where $\beta = \frac{1}{p - 1}$ and $|u|$ is bounded. This article is a remark for their work and we will show when $u \geq 0$, the boundedness condition for $|u|$ can be removed.

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Wangzhe Wu. 2025-04-22. A remark for characterizing blowup introduced by Giga and Kohn. https://arxiv.org/abs/2504.15639

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