Stochastic Homogenization of Monotone Systems of Viscous Hamilton-Jacobi Equations with Convex Nonlinearities

2012/05/08 by Benjamin J. Fehrman, Fehrman, Benjamin J.
Mathematics · #35B27 #35B30 #35G55 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B27 #msc:35B30 #msc:35G55

paper · pdf · doi:10.48550/arxiv.1205.1581

30 pages

arxiv created 2012/05/08 · arxiv updated 2012/05/09

Abstract

We consider the homogenization of monotone systems of viscous Hamilton-Jacobi equations with convex nonlinearities set in the stationary, ergodic setting. The primary focus of this paper is on collapsing systems which, as the microscopic scale tends to zero, average to a deterministic scalar Hamilton-Jacobi equation. However, our methods also apply to systems which do not collapse and, as the microscopic scale tends to zero, average to a deterministic system of Hamilton-Jacobi equations.

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