Convergence of Solutions of the Porous Medium Equation with Reactions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916127055020032 |
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| author | Lou, Bendong Zhou, Maolin |
| author_facet | Lou, Bendong Zhou, Maolin |
| contents | Consider the Cauchy problem of one dimensional porous medium equation (PME) with reactions. We first prove a general convergence result, that is, any bounded global solution starting at a nonnegative compactly supported initial data converges as $t\to \infty$ to a nonnegative zero of the reaction term or a ground state stationary solution. Based on it, we give out a complete classification on the asymptotic behaviors of the solutions for PME with monostable, bistable and combustion types of nonlinearities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_00001 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Convergence of Solutions of the Porous Medium Equation with Reactions Lou, Bendong Zhou, Maolin Analysis of PDEs 35K65, 35K57, 35B40, 35K15 Consider the Cauchy problem of one dimensional porous medium equation (PME) with reactions. We first prove a general convergence result, that is, any bounded global solution starting at a nonnegative compactly supported initial data converges as $t\to \infty$ to a nonnegative zero of the reaction term or a ground state stationary solution. Based on it, we give out a complete classification on the asymptotic behaviors of the solutions for PME with monostable, bistable and combustion types of nonlinearities. |
| title | Convergence of Solutions of the Porous Medium Equation with Reactions |
| topic | Analysis of PDEs 35K65, 35K57, 35B40, 35K15 |
| url | https://arxiv.org/abs/2211.00001 |