Stochastic homogenization of Hamilton–Jacobi equations and some applications
Panagiotis E. Souganidis · Asymptotic Analysis · 1999
Homogenization‐type results for the Cauchy problem for first‐order PDE (Hamilton–Jacobi equations) are presented. The main assumption is that the Hamiltonian is superlinear and convex with respect to the gradient and stationary and ergodic with respect to the spatial variable. Some of applications to related problems as well as to the asymptotics of reaction–diffusion equations and turbulent combustion are also presented.