Scaling limits and homogenization of mixing Hamilton-Jacobi equations
Analysis of PDEs
2020-09-25 v3 Probability
Abstract
We study the homogenization of nonlinear, first-order equations with highly oscillatory mixing spatio-temporal dependence. It is shown in a variety of settings that the homogenized equations are stochastic Hamilton-Jacobi equations with deterministic, spatially homogenous Hamiltonians driven by white noise in time. The paper also contains proofs of some general regularity and path stability results for stochastic Hamilton-Jacobi equations, which are needed to prove some of the homogenization results and are of independent interest.
Keywords
Cite
@article{arxiv.1909.11475,
title = {Scaling limits and homogenization of mixing Hamilton-Jacobi equations},
author = {Benjamin Seeger},
journal= {arXiv preprint arXiv:1909.11475},
year = {2020}
}
Comments
35 pages. The paper has been slightly restructured and condensed