Homogenization for Space-Time-Dependent KPP Reaction-Diffusion Equations and G-Equations
Analysis of PDEs
2022-03-03 v2
Abstract
We prove stochastic homogenization for reaction-advection-diffusion equations with random space-time-dependent KPP reactions with temporal correlations that are decaying in an appropriate sense. We show that the limiting homogenized dynamic has the simple form of spreading with some deterministic direction-dependent speeds from the support of the initial datum. We obtain analogous results for G-equations with random flame speeds and incompressible background advections. Important ingredients in our proofs are a non-autonomous subadditive theorem and the principle of virtual linearity for KPP reactions from the companion papers [30, 35].
Cite
@article{arxiv.2202.08254,
title = {Homogenization for Space-Time-Dependent KPP Reaction-Diffusion Equations and G-Equations},
author = {Yuming Paul Zhang and Andrej Zlatos},
journal= {arXiv preprint arXiv:2202.08254},
year = {2022}
}