Open AccessHamilton’s gradient estimate for fast diffusion equations under geometric flow
Author(s) -
Ghodratallah Fasihi-Ramandi
Publication year - 2019
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2019.3.497
Subject(s) - geometric flow , mathematics , balanced flow , dimension (graph theory) , riemannian manifold , flow (mathematics) , manifold (fluid mechanics) , diffusion , mathematical analysis , geometry , mathematical physics , physics , pure mathematics , thermodynamics , engineering , mechanical engineering
Suppose that M is a complete noncompact Riemannian manifold of dimension n. 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}
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