Abstract for the talk on 18.12.2018 (15:15 h)

Arbeitsgemeinschaft ANGEWANDTE ANALYSIS

Ben Seeger (University of Chicago)
Scaling limits and homogenization for mixing Hamilton-Jacobi equations

I will present results about scaling limits of Hamilton-Jacobi

equations with highly oscillatory, mixing spatio-temporal dependence. When

the Hamiltonian is centered, then the long time, large space behavior of

the solutions is governed by a spatially homogenous, stochastic

Hamilton-Jacobi equation. The result relies on explicit convergence rates

for the stochastic homogenization of Hamilton-Jacobi equations and new

stability estimates for stochastic viscosity solutions. I will also

discuss a class of problems for which the hyperbolic scaling limit leads

to spatio-temporal stochastic homogenization.