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Stochastic homogenization of Hamilton-Jacobi equations in stationary ergodic spatio-temporal media. (English) Zbl 1180.35082
This paper is devoted to the homogenization process of a class of convex Hamilton-Jacobi equations in spatio-temporal stationary ergodic media. The main obstruction to proving homogenization results for this problem, with respect to time and space variables simultaneously, is the lack of a priori regularity of the solutions; this difficulty is overcome here. The author considers a perturbed problem with an appropriate Hamiltonian, for which the homogenization is performed by already known methods. The properties of the homogenized approximating problem complete the study.

MSC:
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
47A35 Ergodic theory of linear operators
35F21 Hamilton-Jacobi equations
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