Homogenization for Space-Time-Dependent KPP Reaction-Diffusion Equations and G-Equations

Yuming Paul Zhang; Andrej Zlatos

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arXiv · 2202.08254

Homogenization for Space-Time-Dependent KPP Reaction-Diffusion Equations and G-Equations

Yuming Paul Zhang·Andrej Zlatos

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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].

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Yuming Paul Zhang, Andrej Zlatos. 2022-02-16. Homogenization for Space-Time-Dependent KPP Reaction-Diffusion Equations and G-Equations. https://arxiv.org/abs/2202.08254

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