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In this paper, we prove some new local Aronson-Benilan type gradient estimates for positive solutions of the porous medium equation \begin{document}$u_{t}=Δ u^{m}, m>1$ \end{document} coupled with Ricci flow, assuming that… Click to show full abstract
In this paper, we prove some new local Aronson-Benilan type gradient estimates for positive solutions of the porous medium equation \begin{document}$u_{t}=Δ u^{m}, m>1$ \end{document} coupled with Ricci flow, assuming that the Ricci curvature is bounded. As application, the related Harnack inequality is derived. Our results generalize known results. These results may be regarded as the generalizations of the gradient estimates of Lu-Ni-Vazquez-Villani and Huang-Huang-Li to the Ricci flow.
Keywords:
gradient estimates;
harnack inequality;
local aronson;
ricci flow;
medium equation;
porous medium
Journal Title: Communications on Pure and Applied Analysis
Year Published: 2018
Link to full text (if available)
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Journal Title: Communications on Pure and Applied Analysis
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!