Stochastic homogenization of viscous superquadratic Hamilton-Jacobi equations in dynamic random environment
Analysis of PDEs
2017-02-07 v2 Optimization and Control
Probability
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.
Keywords
Cite
@article{arxiv.1606.06409,
title = {Stochastic homogenization of viscous superquadratic Hamilton-Jacobi equations in dynamic random environment},
author = {Wenjia Jing and Panagiotis E. Souganidis and Hung V. Tran},
journal= {arXiv preprint arXiv:1606.06409},
year = {2017}
}
Comments
20 pages