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Probability and Combinatorics

Tuesday, April 16, 2019 - 3:00pm

Jessica Lin

McGill

Location

Temple University

Wachman Hall 617

 I will present several results concerning the stochastic homogenization for reaction-diffusion equations. We consider reaction-diffusion equations with nonlinear, heterogeneous, stationary-ergodic reaction terms. Under certain hypotheses on the environment, we show that the typical large-time, large-scale behavior of solutions is governed by a deterministic front propagation. Our arguments rely on analyzing a suitable analogue of “first passage times” for solutions of reaction-diffusion equations. In particular, under these hypotheses, solutions of heterogeneous reaction-diffusion equations with front-like initial data become asymptotically front-like with a deterministic speed. This talk is based on joint work with Andrej Zlatos.