# PDE Seminar

## Some results on porous medium equations： regularity and propagation

### 周茂林 博士 (University of New England, Australia )

#### 2016年12月9日13:00-14:00 闵行校区行政楼12楼PDE中心1202报告厅

Abstract. It is well known that for $m>1$, a solution of the porous medium equation $u_t-\Delta u^m=0$ has a free boundary. In this talk, I will introduce two recent results on the free boundary: 1. if the support of the initial datum is convex, then the free boundary is $C^\infty$ smooth; 2. for the nonlinear porous medium equation $u_t-\Delta u^m=u-u^2$, we can give out a sharp estimate on the propagation of the free boundary with radially symmetry initial datum in higher dimensional cases.