Infinite time blow-up and slow decay for the six dimensional energy-critical heat equation with self-similarly decaying initial data
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913054022696960 |
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| author | Hisa, Kotaro Takahashi, Jin Zhanpeisov, Erbol |
| author_facet | Hisa, Kotaro Takahashi, Jin Zhanpeisov, Erbol |
| contents | We consider the six dimensional energy-critical semilinear heat equation with self-similarly decaying initial data. Our main result shows the existence of sign-changing solutions that exhibit infinite-time blow-up and nonnegative solutions that decay strictly more slowly than the self-similar rate. Moreover, the blow-up and decay rates are not uniquely determined by the decay rate of the initial data, but exhibit a certain flexibility depending on the construction. The proof is based on gluing suitably rescaled bubbles to forward self-similar solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20396 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Infinite time blow-up and slow decay for the six dimensional energy-critical heat equation with self-similarly decaying initial data Hisa, Kotaro Takahashi, Jin Zhanpeisov, Erbol Analysis of PDEs 35K58, 35B40, 35B44 We consider the six dimensional energy-critical semilinear heat equation with self-similarly decaying initial data. Our main result shows the existence of sign-changing solutions that exhibit infinite-time blow-up and nonnegative solutions that decay strictly more slowly than the self-similar rate. Moreover, the blow-up and decay rates are not uniquely determined by the decay rate of the initial data, but exhibit a certain flexibility depending on the construction. The proof is based on gluing suitably rescaled bubbles to forward self-similar solutions. |
| title | Infinite time blow-up and slow decay for the six dimensional energy-critical heat equation with self-similarly decaying initial data |
| topic | Analysis of PDEs 35K58, 35B40, 35B44 |
| url | https://arxiv.org/abs/2604.20396 |