Exponential convergence of solutions for random Hamilton-Jacobi equations

被引：2

作者：

Iturriaga, Renato ^{[1
]}

Khanin, Konstantin ^{[2
,3
]}

Zhang, Ke ^{[2
]}

机构：

[1] CIMAT, Guanajuato, Mexico

[2] Univ Toronto, Toronto, ON, Canada

[3] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow, Russia

来源：

STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS | 2020年 / 8卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Hamilton-Jacobi equation; Burger's equation; Stochastic PDE; BURGERS-EQUATION; HYPERBOLICITY;

D O I：

10.1007/s40072-019-00153-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that for a family of randomly kicked Hamilton-Jacobi equations on the torus, almost surely, the solution of an initial value problem converges exponentially fast to the unique stationary solution. Combined with the earlier results of the authors, this completes the program in the multi-dimensional setting started by E, Khanin, Mazel and Sinai in the one-dimensional case.

引用

页码：544 / 579

页数：36

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