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Stochastic homogenization of Hamilton-Jacobi equations and some applications. (English) Zbl 0935.35008
Under the assumptions that the Hamiltionian is superlinear and convex with respect to the gradient, stationary and ergodic with respect to the spatial variable, homogenization-type results for the stochastic Cauchy problem for the Hamilton-Jacobi equation are given. The results of the paper are further applied to the study of the asymptotics of reaction-diffusion equations and turbulent combustion.
Also a brief review of the classical viscosity theory approach to homogenization is given, and the differences between the general stochastic case and a deterministic one are pointed out.

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35F10 Initial value problems for linear first-order PDEs
35K57 Reaction-diffusion equations