Sharp non-explicit blow-up profile for perturbed nonlinear heat equations with gradient terms
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908829546971136 |
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| author | Boughrara, Maissâ |
| author_facet | Boughrara, Maissâ |
| contents | We consider a class of blow-up solutions for perturbed nonlinear heat equations involving gradient terms. We first prove the single point blow-up property for this equation and determine its final blow-up profile. We also give a sharper description of its blow-up behaviour, where we take as a profile some suitably chosen solution of the unperturbed semilinear heat equation. The proof relies on selfsimilar variables with involved arguments to control the gradient term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06620 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sharp non-explicit blow-up profile for perturbed nonlinear heat equations with gradient terms Boughrara, Maissâ Analysis of PDEs 35A20, 35B40, 35K55 We consider a class of blow-up solutions for perturbed nonlinear heat equations involving gradient terms. We first prove the single point blow-up property for this equation and determine its final blow-up profile. We also give a sharper description of its blow-up behaviour, where we take as a profile some suitably chosen solution of the unperturbed semilinear heat equation. The proof relies on selfsimilar variables with involved arguments to control the gradient term. |
| title | Sharp non-explicit blow-up profile for perturbed nonlinear heat equations with gradient terms |
| topic | Analysis of PDEs 35A20, 35B40, 35K55 |
| url | https://arxiv.org/abs/2310.06620 |