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.
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页码：5151 / 5162
页数：12
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