Quantitative Homogenization for Combustion in Random Media
Analysis of PDEs
2021-07-27 v1
Abstract
We obtain the first quantitative stochastic homogenization result for reaction-diffusion equations, for ignition reactions in dimensions that either have finite ranges of dependence or are close enough to such reactions, and for solutions with initial data that approximate characteristic functions of general convex sets. We show algebraic rate of convergence of these solutions to their homogenized limits, which are (discontinuous) viscosity solutions of certain related Hamilton-Jacobi equations.
Keywords
Cite
@article{arxiv.2107.12174,
title = {Quantitative Homogenization for Combustion in Random Media},
author = {Yuming Paul Zhang and Andrej Zlatos},
journal= {arXiv preprint arXiv:2107.12174},
year = {2021}
}