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Aronson-B\’{e}nilan estimates for weighted porous medium equations under the geometric flow
  • shahroud azami
shahroud azami
Imam Khomeini International University

Corresponding Author:[email protected]

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In this paper, we study Aronson-B\’{e}nilan gradient estimates for positive solutions of weighted porous medium equations $$\partial_{t}u(x,t)=\Delta_{\phi}u^{p}(x,t),\,\,\,\,(x,t)\in M\times[0,T]$$ coupled with the geometric flow $\frac{\partial g}{\partial t}=2h(t),\,\,\,\frac{\partial \phi}{\partial t}=\Delta \phi$ on a complete measure space $(M^{n},g,e^{-\phi}dv)$. As an application, by integrating the gradient estimates, we derive the corresponding Harnack inequalities.
21 Nov 2021Submitted to Mathematical Methods in the Applied Sciences
23 Nov 2021Submission Checks Completed
23 Nov 2021Assigned to Editor
28 Nov 2021Reviewer(s) Assigned
17 May 2022Review(s) Completed, Editorial Evaluation Pending
17 May 2022Editorial Decision: Revise Minor
27 Jul 20221st Revision Received
28 Jul 2022Submission Checks Completed
28 Jul 2022Assigned to Editor
28 Jul 2022Reviewer(s) Assigned
22 Dec 2022Review(s) Completed, Editorial Evaluation Pending
27 Dec 2022Editorial Decision: Accept