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arXiv · 1606.06409

Stochastic homogenization of viscous superquadratic Hamilton-Jacobi equations in dynamic random environment

Wenjia Jing·Panagiotis E. Souganidis·Hung V. Tran
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Abstract

We study the qualitative homogenization of second order viscous Hamilton-Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is convex and superquadratic in the momentum variable (gradient) we establish a homogenization result and characterize the effective Hamiltonian for arbitrary (possibly degenerate) elliptic diffusion matrices. The result extends previous work that required uniform ellipticity and space-time homogeneity for the diffusion.

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Wenjia Jing, Panagiotis E. Souganidis, Hung V. Tran. 2017-02-06. Stochastic homogenization of viscous superquadratic Hamilton-Jacobi equations in dynamic random environment. https://doi.org/10.1186/s40687-016-0090-9

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