AIMS Mathematics, 2019, 4(3): 497-505. doi: 10.3934/math.2019.3.497

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Hamilton’s gradient estimate for fast diffusion equations under geometric flow

Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran

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\[ \dfrac{\partial u}{\partial t}=\Delta u^m ,\qquad 1-\dfrac{4}{n+8}<m<1\]on $M\times (-\infty ,0]$ under the geometric flow.
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