Aronson-B\’{e}nilan estimates for weighted porous medium equations under the geometric flow
| Autor: | Shahroud Azami |
|---|---|
| Rok vydání: | 2021 |
| DOI: | 10.22541/au.163810706.69950528/v1 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|