##### Department of Mathematics,

University of California San Diego

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### Math 248 - Real Analysis Seminar

## Yuming Zhang

#### UCLA

## Porous Medium Equation with a Drift: Free Boundary Regularity

##### Abstract:

We study regularity properties of the free boundary for solutions of the porous medium equation with the presence of drift. We show that if the initial data has super-quadratic growth at the free boundary, then the support strictly expands relative to the streamline, and that the movement is Holder continuous in time. Under additional information of directional monotonicity in space, we derive nondegeneracy of solutions and $C^{1,\alpha}$ regularity of free boundaries. Finally several examples of singularities are given that illustrate differences from the zero drift case.

Host: Andrej Zlatos

### October 23, 2018

### 9:45 AM

### AP&M 7321

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