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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2510.17718 |
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| _version_ | 1866912660911554560 |
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| author | Duan, Senhao |
| author_facet | Duan, Senhao |
| contents | In this paper, we prove the existence of a singular standing sphere blow-up solution for the nonlinear heat equation with radial symmetry. This solution develops a finite-time singularity on a fixed-radius sphere and exhibits a flat blow-up profile. Our construction refines the method developed by Merle and Zaag \cite{MZJEMS24} which reduces the infinite-dimensional dynamics to a finite-dimensional problem in radial case. The solution satisfies explicit asymptotics near the singular ring and remains regular elsewhere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17718 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Flat Standing Sphere Blow-up Solutions for the Nonlinear Heat Equation Duan, Senhao Analysis of PDEs 35A21 35B44 35K55 In this paper, we prove the existence of a singular standing sphere blow-up solution for the nonlinear heat equation with radial symmetry. This solution develops a finite-time singularity on a fixed-radius sphere and exhibits a flat blow-up profile. Our construction refines the method developed by Merle and Zaag \cite{MZJEMS24} which reduces the infinite-dimensional dynamics to a finite-dimensional problem in radial case. The solution satisfies explicit asymptotics near the singular ring and remains regular elsewhere. |
| title | Flat Standing Sphere Blow-up Solutions for the Nonlinear Heat Equation |
| topic | Analysis of PDEs 35A21 35B44 35K55 |
| url | https://arxiv.org/abs/2510.17718 |