Some gradient estimates and Liouville properties of the fast diffusion equation on Riemannian manifolds
type: Item
instance of: scholarly article
title: Some gradient estimates and Liouville properties of the fast diffusion equation on Riemannian manifolds
zbMATH Open document ID: 1473.58022
author: W. Wang
author: Pan Zhang
author: Rulong Xie
published in: Chinese Annals of Mathematics. Series B
publication date: 2021-08-19T00:00:00Z
review text: 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 \(\alpha=1\).
reviewed by: Feng-Yu Wang
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 53E20
zbMATH DE Number: 7383602
zbMATH Keywords: gradient estimate
zbMATH Keywords: fast diffusion equation
zbMATH Keywords: Ricci flow
zbMATH Keywords: Liouville theorem
MaRDI profile type: Publication
full work available at URL: s11401-021-0276-3
OpenAlex ID: W3197058493
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Wikidata QID: Q115379268
DOI: 10.1007/S11401-021-0276-3
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description: scientific article; zbMATH DE number 7383602