Quantitative homogenization for combustion in random media

  • Yuming Paul Zhang

    Auburn University, United States of America
  • Andrej Zlatoš

    University of California San Diego, La Jolla, United States of America
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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 an algebraic rate of convergence of these solutions to their homogenized limits, which are (discontinuous) viscosity solutions of certain related Hamilton–Jacobi equations.

Cite this article

Yuming Paul Zhang, Andrej Zlatoš, Quantitative homogenization for combustion in random media. Ann. Inst. H. Poincaré Anal. Non Linéaire 41 (2024), no. 4, pp. 853–876

DOI 10.4171/AIHPC/80