##### Department of Mathematics,

University of California San Diego

****************************

### Math 248 - Seminar in Real Analysis

## Yuming Paul Zhang

#### UCSD

## Homogenization for combustion in random media

##### Abstract:

We study long time dynamics of combustive processes in random media, modeled by reaction-diffusion equations with random ignition reactions. One expects that under reasonable hypotheses on the randomness, large scale dynamics of solutions to these equations is almost surely governed by a homogeneous Hamilton-Jacobi equation. While this was previously shown in one dimension as well as for radially symmetric reactions in several dimensions, we prove this phenomenon in the general non-isotropic multidimensional setting. We also show that the rate of convergence of solutions to the Hamilton-Jacobi dynamics is at least algebraic in the relevant space-time scales when the initial data is close to an indicator function of a convex set. This talk is based on joint work with Andrej Zlato\v{s}.

### October 12, 2021

### 11:00 AM

https://ucsd.zoom.us/j/99515535778

****************************