A PDE Approach to Large-Time Asymptotics for Boundary-Value Problems for Nonconvex Hamilton-Jacobi Equations

被引：13

作者：

Barles, Guy ^{[1
]}

Mitake, Hiroyoshi ^{[2
]}

机构：

[1] Univ Tours, UMR CNRS 6083, Lab Math & Phys Theor, F-37200 Tours, France

[2] Hiroshima Univ, Grad Sch Engn, Dept Appl Math, Higashihiroshima 724, Japan

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2012年 / 37卷 / 01期

关键词：

Ergodic problem; Hamilton-Jacobi equations; Initial-boundary value problem; Large-time behavior; Nonconvex Hamiltonian; CONVEX HAMILTONIANS; DIFFERENTIAL-EQUATIONS; VISCOSITY SOLUTIONS; PERIODIC-SOLUTIONS; STATE CONSTRAINTS; BEHAVIOR; CONVERGENCE;

D O I：

10.1080/03605302.2011.553645

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the large-time behavior of three types of initial-boundary value problems for Hamilton-Jacobi Equations with nonconvex Hamiltonians. We consider the Neumann or oblique boundary condition, the state constraint boundary condition and Dirichlet boundary condition. We establish general convergence results for viscosity solutions to asymptotic solutions as time goes to infinity via an approach based on PDE techniques. These results are obtained not only under general conditions on the Hamiltonians but also under weak conditions on the domain and the oblique direction of reflection in the Neumann case.

引用

页码：136 / 168

页数：33

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