Stochastic homogenization of viscous superquadratic Hamilton-Jacobi equations in dynamic random environment

被引：7

作者：

Jing, Wenjia ^{[1
]}

Souganidis, Panagiotis E. ^{[1
]}

Tran, Hung V. ^{[2
]}

机构：

[1] Univ Chicago, Dept Math, 5734 S Univ Ave, Chicago, IL 60637 USA

[2] Univ Wisconsin, Dept Math, Van Vleck Hall,480 Lincoln Dr, Madison, WI 53706 USA

来源：

RESEARCH IN THE MATHEMATICAL SCIENCES | 2017年 / 4卷

基金：

美国国家科学基金会;

关键词：

Stochastic homogenization; Hamilton-Jacobi equations; Viscosity solutions; Dynamic random environment; Time-dependent Hamiltonian; Convex analysis; VISCOSITY SOLUTIONS; TIME;

D O I：

10.1186/s40687-016-0090-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the qualitative homogenization of second-order 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.

引用

页数：20

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