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

页码：5392 / 5405

页数：14

共 23 条

[1]

Bardi M., 1997, SYSTEMS CONTROL FDN

[2]

BARLES G, 1987, ESAIM-MATH MODEL NUM, V21, P557

[3] On the large time behavior of solutions of Hamilton-Jacobi equations [J].

Barles, G ;

Souganidis, PE .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2000, 31 (04) :925-939

[4] Ergodic type problems and large time behaviour of unbounded solutions of Hamilton-Jacobi Equations [J].

Barles, Guy ;

Roquejoffre, Jean-Michel .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2006, 31 (08) :1209-1225

[5] Convergence to time-periodic solutions in time-periodic Hamilton-Jacobi equations on the circle [J].

Bernard, P ;

Roquejoffre, JM .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2004, 29 (3-4) :457-469

[6] Time periodic viscosity solutions of Hamilton-Jacobi equations [J].

Bostan, Mihai ;

Namah, Gawtum .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2007, 6 (02) :389-410

[7] A generalized dynamical approach to the large time behavior of solutions of Hamilton-Jacobi equations [J].

Davini, Andrea ;

Siconolfi, Antonio .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2006, 38 (02) :478-502

[8] PDE aspects of Aubry-Mather theory for quasiconvex Hamiltonians [J].

Fathi, A ;

Siconolfi, A .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2005, 22 (02) :185-228

[9] On convergence of the Lax-Oleinik semi-group [J].

Fathi, A .

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1998, 327 (03) :267-270

[10] Asymptotic solutions of Hamilton-Jacobi equations in Euclidean n space [J].

Fujita, Yasuhiro ;

Ishii, Hitoshi ;

Loreti, Paola .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2006, 55 (05) :1671-1700

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