Large time behavior of solutions of Hamilton-Jacobi equations with periodic boundary data

被引：13
作者：
Mitake, Hiroyoshi [1 ]
机构：
[1] Waseda Univ, Dept Pure & Appl Math, Shinjuku Ku, Tokyo 1698555, Japan
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 11期
关键词：
Large-time behavior; Hamilton-Jacobi equations; Cauchy-Dirichlet problem; Periodic solution; Aubry set; EUCLIDEAN-N-SPACE; ASYMPTOTIC SOLUTIONS; CONVEX HAMILTONIANS; CONVERGENCE;
D O I：
10.1016/j.na.2009.04.028
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the large time behavior of viscosity solutions of Hamilton-Jacobi equations with periodic boundary data on bounded domains. We establish a result on convergence of viscosity solutions to state constraint asymptotic solutions or periodic asymptotic solutions depending on the sign of critical value as time goes to infinity. (C) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码：5392 / 5405
页数：14
相关论文
共 23 条
[11]  
ICHIHARA N, ARCH RATION IN PRESS
[12]   Asymptotic solutions of Hamilton-Jacobi equations with semi-periodic Hamiltonians [J].
Ichihara, Naoyuki ;
Ishii, Hitoshi .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2008, 33 (05) :784-807
[13]  
Ichihara N, 2008, METHODS APPL ANAL, V15, P223
[14]  
Ishii H., 1989, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), V16, P105
[15]   Asymptotic solutions for large time of Hamilton-Jacobi equations in Euclidean n space [J].
Ishii, Hitoshi .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2008, 25 (02) :231-266
[16]   Representation formulas for solutions of Hamilton-Jacobi equations with convex Hamiltonians [J].
Ishii, Hitoshi ;
Mitake, Hiroyoshi .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2007, 56 (05) :2159-2183
[17]  
Lions P.-L., 1982, RES NOTES MATH, V69
[18]   The large-time behavior of solutions of the Cauchy-Dirichlet problem for Hamilton-Jacobi equations [J].
Mitake, Hiroyoshi .
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2008, 15 (03) :347-362
[19]   Asymptotic Solutions of Hamilton-Jacobi Equations with State Constraints [J].
Mitake, Hiroyoshi .
APPLIED MATHEMATICS AND OPTIMIZATION, 2008, 58 (03) :393-410
[20]   Remarks on the long time behaviour of the solutions of Hamilton-Jacobi equations [J].
Namah, G ;
Roquejoffre, JM .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1999, 24 (5-6) :883-893
123