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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:300

Article

Yilmaz, Atilla¹ 

[1] Temple Univ, Dept Math, 1805 N Broad St, Philadelphia, PA 19122 USA

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

DOI  :  10.1016/j.jde.2021.08.004

来源: Elsevier

【 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.

【 授权许可】

Free