Abstract for the talk on 18.12.2018 (15:15 h)
Arbeitsgemeinschaft ANGEWANDTE ANALYSISBen 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.