Hamilton’s gradient estimate for fast diffusion equations under geometric flow
Suppose that <em>M</em> is a complete noncompact Riemannian manifold of dimension <em>n</em>. In the present paper, we obtain a Hamilton's gradient estimate for positive solutions of the fast diffusion equations\[ \dfrac{\partial u}{\partial t}=\Delta u^m ,\qquad 1-\dfra...
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| Format: | Article |
| Language: | English |
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AIMS Press
2019-05-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2019.3.497/fulltext.html |
| _version_ | 1811214259834585088 |
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| author | Ghodratallah Fasihi-Ramandi |
| author_facet | Ghodratallah Fasihi-Ramandi |
| author_sort | Ghodratallah Fasihi-Ramandi |
| collection | DOAJ |
| description | Suppose that <em>M</em> is a complete noncompact Riemannian manifold of dimension <em>n</em>. In the present paper, we obtain a Hamilton's gradient estimate for positive solutions of the fast diffusion equations\[ \dfrac{\partial u}{\partial t}=\Delta u^m ,\qquad 1-\dfrac{4}{n+8}<m<1\]on $M\times (-\infty ,0]$ under the geometric flow. |
| first_indexed | 2024-04-12T06:00:14Z |
| format | Article |
| id | doaj.art-4af90454d4ad425ebf052d751c1359e8 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-12T06:00:14Z |
| publishDate | 2019-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-4af90454d4ad425ebf052d751c1359e82022-12-22T03:45:03ZengAIMS PressAIMS Mathematics2473-69882019-05-014349750510.3934/math.2019.3.497Hamilton’s gradient estimate for fast diffusion equations under geometric flowGhodratallah Fasihi-Ramandi0Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, IranSuppose that <em>M</em> is a complete noncompact Riemannian manifold of dimension <em>n</em>. In the present paper, we obtain a Hamilton's gradient estimate for positive solutions of the fast diffusion equations\[ \dfrac{\partial u}{\partial t}=\Delta u^m ,\qquad 1-\dfrac{4}{n+8}<m<1\]on $M\times (-\infty ,0]$ under the geometric flow.https://www.aimspress.com/article/10.3934/math.2019.3.497/fulltext.htmlfast diffusion equationRicci flowHamilton inequalitygradient estimates |
| spellingShingle | Ghodratallah Fasihi-Ramandi Hamilton’s gradient estimate for fast diffusion equations under geometric flow AIMS Mathematics fast diffusion equation Ricci flow Hamilton inequality gradient estimates |
| title | Hamilton’s gradient estimate for fast diffusion equations under geometric flow |
| title_full | Hamilton’s gradient estimate for fast diffusion equations under geometric flow |
| title_fullStr | Hamilton’s gradient estimate for fast diffusion equations under geometric flow |
| title_full_unstemmed | Hamilton’s gradient estimate for fast diffusion equations under geometric flow |
| title_short | Hamilton’s gradient estimate for fast diffusion equations under geometric flow |
| title_sort | hamilton s gradient estimate for fast diffusion equations under geometric flow |
| topic | fast diffusion equation Ricci flow Hamilton inequality gradient estimates |
| url | https://www.aimspress.com/article/10.3934/math.2019.3.497/fulltext.html |
| work_keys_str_mv | AT ghodratallahfasihiramandi hamiltonsgradientestimateforfastdiffusionequationsundergeometricflow |