Some gradient estimates and Liouville properties of the fast diffusion equation on Riemannian manifolds (Q2047227)
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scientific article; zbMATH DE number 7383602
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some gradient estimates and Liouville properties of the fast diffusion equation on Riemannian manifolds |
scientific article; zbMATH DE number 7383602 |
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Some gradient estimates and Liouville properties of the fast diffusion equation on Riemannian manifolds (English)
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19 August 2021
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Let \(\Delta_t\) be the Laplacian associated with a Ricci flow and consider the fast diffusion equation \[\partial_t u_t= \Delta_t u_t^\alpha\] for \(\alpha\in (0,1).\) The Li-Yau type gradient estimate as well as Liouville theorem are established for positive solutions to this equation, which extend some existing results derived for the heat equation where \(\alpha=1\).
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gradient estimate
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fast diffusion equation
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Ricci flow
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Liouville theorem
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