Stochastic homogenization of a class of quasiconvex viscous Hamilton-Jacobi equations in one space dimension

[摘要] We prove homogenization for a class of viscous Hamilton-Jacobi equations in the stationary & ergodic setting in one space dimension. Our assumptions include most notably the following: the Hamiltonian is of the form G(p) + beta V (x, omega), the function G is coercive and strictly quasiconvex, min G = 0, beta > 0, the random potential V takes values in [0, 1] with full support and it satisfies a hill condition that involves the diffusion coefficient. Our approach is based on showing that, for every direction outside of a bounded interval (theta(1)(beta), theta(2)(beta)), there is a unique sublinear corrector with certain properties. We obtain a formula for the effective Hamiltonian and deduce that it is coercive, identically equal to beta on (theta(1)(beta),theta(2)(beta)), and strictly monotone elsewhere. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-11-05

[关键词] Stochastic homogenization;Viscous Hamilton-Jacobi equation;Quasiconvexity;Viscosity solution;Corrector;Scaled hill condition