Homogenization of “Viscous” Hamilton–Jacobi Equations in Stationary Ergodic Media
Pierre‐Louis Lions, Panagiotis E. Souganidis · Communications in Partial Differential Equations · 2005
We study the homogenization of “viscous” Hamilton–Jacobi equations in stationary ergodic media. The “viscosity” and the spatial oscillations are assumed to be of the same order. We identify the asymptotic (effective) equation, which is a first-order deterministic Hamilton–Jacobi equation. We also provide examples that show that the associated macroscopic problem does not admit suitable solutions (correctors). Finally, we present as applications results about large deviations of diffusion processes and front propagation (asymptotics of reaction-diffusion equations) in random environments.