Semi-linear evolution equations via positive semigroups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909454230880256 |
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| author | Arendt, Wolfgang Daners, Daniel |
| author_facet | Arendt, Wolfgang Daners, Daniel |
| contents | We study semi-linear evolutionary problems where the linear part is the generator of a positive $C_0$-semigroup. The non-linear part is assumed to be quasi-increasing. Given an initial value in between a sub- and a super-solution of the stationary problem we find a solution of the semi-linear evolutionary problem. Convergence as $t\to\infty$ is also studied for the solutions. Our results are applied to the logistic equation with diffusion, to a Lotka-Volterra competition model and the Fisher equation from population genetics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05522 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semi-linear evolution equations via positive semigroups Arendt, Wolfgang Daners, Daniel Analysis of PDEs 34G20 (Primary) 34G20, 47N20, 47H07, 35K20 (Secondary) We study semi-linear evolutionary problems where the linear part is the generator of a positive $C_0$-semigroup. The non-linear part is assumed to be quasi-increasing. Given an initial value in between a sub- and a super-solution of the stationary problem we find a solution of the semi-linear evolutionary problem. Convergence as $t\to\infty$ is also studied for the solutions. Our results are applied to the logistic equation with diffusion, to a Lotka-Volterra competition model and the Fisher equation from population genetics. |
| title | Semi-linear evolution equations via positive semigroups |
| topic | Analysis of PDEs 34G20 (Primary) 34G20, 47N20, 47H07, 35K20 (Secondary) |
| url | https://arxiv.org/abs/2407.05522 |