Boundedness of solutions of nonautonomous degenerate logistic equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916116778975232 |
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| author | Arrieta, José M. Molina-Rodríguez, Marcos Santos, Lucas A. |
| author_facet | Arrieta, José M. Molina-Rodríguez, Marcos Santos, Lucas A. |
| contents | In this work we analyze the boundedness properties of the solutions of a nonautonomous parabolic degenerate logistic equation in a bounded domain. The equation is degenerate in the sense that the logistic nonlinearity vanishes in a moving region, $K(t)$, inside the domain. The boundedness character of the solutions depends not only on, roughly speaking, the first eigenvalue of the Laplace operator in $K(t)$ but also on the way this moving set evolves inside the domain and in particular on the speed at which it moves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07571 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Boundedness of solutions of nonautonomous degenerate logistic equations Arrieta, José M. Molina-Rodríguez, Marcos Santos, Lucas A. Analysis of PDEs 35B40, 35K57 In this work we analyze the boundedness properties of the solutions of a nonautonomous parabolic degenerate logistic equation in a bounded domain. The equation is degenerate in the sense that the logistic nonlinearity vanishes in a moving region, $K(t)$, inside the domain. The boundedness character of the solutions depends not only on, roughly speaking, the first eigenvalue of the Laplace operator in $K(t)$ but also on the way this moving set evolves inside the domain and in particular on the speed at which it moves. |
| title | Boundedness of solutions of nonautonomous degenerate logistic equations |
| topic | Analysis of PDEs 35B40, 35K57 |
| url | https://arxiv.org/abs/2310.07571 |