A triviality result for semilinear parabolic equations
We show a triviality result for "pointwise" monotone in time, bounded "eternal" solutions of the semilinear heat equation $ \begin{equation*} u_{t} = \Delta u + |u|^{p} \end{equation*} $ on complete Riemannian manifolds of dimension $ n \geq 5 $ with nonnegative Ricci tensor, whe...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-01-01
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| Series: | Mathematics in Engineering |
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| Online Access: | https://aimspress.com/article/doi/10.3934/mine.2022002?viewType=HTML |
| _version_ | 1818333567636209664 |
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| author | Daniele Castorina Giovanni Catino Carlo Mantegazza |
| author_facet | Daniele Castorina Giovanni Catino Carlo Mantegazza |
| author_sort | Daniele Castorina |
| collection | DOAJ |
| description | We show a triviality result for "pointwise" monotone in time, bounded "eternal" solutions of the semilinear heat equation $ \begin{equation*} u_{t} = \Delta u + |u|^{p} \end{equation*} $ on complete Riemannian manifolds of dimension $ n \geq 5 $ with nonnegative Ricci tensor, when $ p $ is smaller than the critical Sobolev exponent $ \frac{n+2}{n-2} $. |
| first_indexed | 2024-12-13T13:53:42Z |
| format | Article |
| id | doaj.art-fd89ba2ef6094591a24359db3256d5f1 |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-12-13T13:53:42Z |
| publishDate | 2022-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-fd89ba2ef6094591a24359db3256d5f12022-12-21T23:42:59ZengAIMS PressMathematics in Engineering2640-35012022-01-014111510.3934/mine.2022002A triviality result for semilinear parabolic equationsDaniele Castorina 0Giovanni Catino1Carlo Mantegazza21. Dipartimento di Matematica e Applicazioni, Università di Napoli, Via Cintia, Monte S. Angelo 80126 Napoli, Italy2. Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy1. Dipartimento di Matematica e Applicazioni, Università di Napoli, Via Cintia, Monte S. Angelo 80126 Napoli, ItalyWe show a triviality result for "pointwise" monotone in time, bounded "eternal" solutions of the semilinear heat equation $ \begin{equation*} u_{t} = \Delta u + |u|^{p} \end{equation*} $ on complete Riemannian manifolds of dimension $ n \geq 5 $ with nonnegative Ricci tensor, when $ p $ is smaller than the critical Sobolev exponent $ \frac{n+2}{n-2} $.https://aimspress.com/article/doi/10.3934/mine.2022002?viewType=HTMLancient solutioneternal solutionsuperlinear heat equation |
| spellingShingle | Daniele Castorina Giovanni Catino Carlo Mantegazza A triviality result for semilinear parabolic equations Mathematics in Engineering ancient solution eternal solution superlinear heat equation |
| title | A triviality result for semilinear parabolic equations |
| title_full | A triviality result for semilinear parabolic equations |
| title_fullStr | A triviality result for semilinear parabolic equations |
| title_full_unstemmed | A triviality result for semilinear parabolic equations |
| title_short | A triviality result for semilinear parabolic equations |
| title_sort | triviality result for semilinear parabolic equations |
| topic | ancient solution eternal solution superlinear heat equation |
| url | https://aimspress.com/article/doi/10.3934/mine.2022002?viewType=HTML |
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