LONG-TIME ASYMPTOTIC SOLUTIONS OF CONVEX HAMILTON-JACOBI EQUATIONS DEPENDING ON UNKNOWN FUNCTIONS

被引：2

作者：

Li, Xia ^{[1
]}

机构：

[1] Suzhou Univ Sci & Technol, Suzhou 215009, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2017年 / 37卷 / 10期

基金：

中国国家自然科学基金;

关键词：

Hamilton-Jacobi equations; viscosity solutions; long-time asymptotic solutions; PDE-viscosity solutions approach; dynamical approach; VISCOSITY SOLUTIONS; BEHAVIOR;

D O I：

10.3934/dcds.2017223

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the long-time asymptotic behaviour of viscosity solutions u(x, t) of the Hamilton-Jacobi equation u(t)(x, t) + H(x,u(x,t), Du(x,t)) = 0 in T-n x (-infinity, infinity), where H = H(x, u, p) is convex and coercive in p and non-decreasing on u, and establish the uniform convergence of u to an an asymptotic solution u infinity as t -> infinity. Moreover, u infinity is a viscosity solution of Hamilton-Jacobi equation H(x, u(x), Du(x)) = 0.

引用

页码：5151 / 5162

页数：12

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