Uniform boundedness and blow-up rate of solutions in non-scale-invariant superlinear heat equations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929651488653312 |
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| author | Fujishima, Yohei Kan, Toru |
| author_facet | Fujishima, Yohei Kan, Toru |
| contents | For superlinear heat equations with the Dirichlet boundary condition, the $L^\infty$ estimates of radially symmetric solutions are studied. In particular, the uniform boundedness of global solutions and the non-existence of solutions with type II blow-up are proved. For the space dimension greater than $9$, our results are shown under the condition that an exponent representing the growth rate of a nonlinear term is between the Sobolev exponent and the Joseph-Lundgren exponent. In the case where the space dimension is greater than $2$ and smaller than $10$, our results are applicable for nonlinear terms growing extremely faster than the exponential function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20402 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform boundedness and blow-up rate of solutions in non-scale-invariant superlinear heat equations Fujishima, Yohei Kan, Toru Analysis of PDEs For superlinear heat equations with the Dirichlet boundary condition, the $L^\infty$ estimates of radially symmetric solutions are studied. In particular, the uniform boundedness of global solutions and the non-existence of solutions with type II blow-up are proved. For the space dimension greater than $9$, our results are shown under the condition that an exponent representing the growth rate of a nonlinear term is between the Sobolev exponent and the Joseph-Lundgren exponent. In the case where the space dimension is greater than $2$ and smaller than $10$, our results are applicable for nonlinear terms growing extremely faster than the exponential function. |
| title | Uniform boundedness and blow-up rate of solutions in non-scale-invariant superlinear heat equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.20402 |