A PDE Approach to the Long-Time Asymptotic Solutions of Contact Hamilton-Jacobi Equations

被引：1

作者：

WANG Yujie ^{[1
]}

LI Xia ^{[1
]}

机构：

[1] School of Mathematics Science, Suzhou University of Science and Technology

来源：

Wuhan University Journal of Natural Sciences | 2022年 / 03期

基金：

中国国家自然科学基金;

关键词：

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

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(x,t) +H(x,u(x,t),Du(x,t)) = 0 in T~n×(0,∞) with a PDE approach, where H = H(x,u,p) is coercive in p, non-decreasing in u and strictly convex in(u,p), and establish the uniform convergence of u(x,t) to an asymptotic solution u(x) as t → ∞. Moreover, uis a viscosity solution of Hamilton-Jacobi equation H(x,u(x),Du(x)) = 0.

引用

页码：189 / 194

页数：6

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