A remark for characterizing blowup introduced by Giga and Kohn
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915253272444928 |
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| author | Wu, Wangzhe |
| author_facet | Wu, Wangzhe |
| contents | Giga and Kohn studied the blowup solutions for the equation $v_{t} - Δv - |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 $Δu - \frac{1}{2} x \cdot \nabla u + |u|^{p - 1} u - βu = 0$ where $β= \frac{1}{p - 1}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15639 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A remark for characterizing blowup introduced by Giga and Kohn Wu, Wangzhe Analysis of PDEs Giga and Kohn studied the blowup solutions for the equation $v_{t} - Δv - |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 $Δu - \frac{1}{2} x \cdot \nabla u + |u|^{p - 1} u - βu = 0$ where $β= \frac{1}{p - 1}$ 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. |
| title | A remark for characterizing blowup introduced by Giga and Kohn |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.15639 |