Stochastic homogenization of Hamilton-Jacobi equations and some applications. (English) Zbl 0935.35008

Souganidis, Panagiotis E.

Asymptotic Anal. 20, No. 1, 1-11 (1999).

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.

Reviewer: W.Kotarski (Sosnowiec)

MSC:

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

Keywords:

viscosity solution; turbulent combustion