On the large time behavior of solutions of Hamilton-Jacobi equations

被引：104

作者：

Barles, G

Souganidis, PE

机构：

[1] Univ Tours, Fac Sci & Tech, Lab Math & Phys Theor, F-37200 Tours, France

[2] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2000年 / 31卷 / 04期

关键词：

Hamilton-Jacobi equations; periodicity; ergodic problem; long time behavior; viscosity solutions; hamiltonian systems;

D O I：

10.1137/S0036141099350869

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the long time behavior of viscosity solutions of first-order Hamilton-Jacobi equations with periodic space dependence. We prove, under sharp conditions, that as time goes to infinity, solutions converge to solutions of the corresponding stationary equation.

引用

页码：925 / 939

页数：15

共 10 条

[1]

[Anonymous], 1994, MATH APPL

[2] Ergodic problem for the Hamilton-Jacobi-Bellman equation .1. Existence of the ergodic attractor [J].

Arisawa, M .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1997, 14 (04) :415-438

[3] Ergodic problem for the Hamilton-Jacobi-Bellman equation. II [J].

Arisawa, M .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1998, 15 (01) :1-24

[4] 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

[5]

Lions P.-L., HOMOGENIZATION HAMIL

[6]

Lions P-L., 1982, GEN SOLUTIONS HAMILT

[7] 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

[8]

ROQUEJOFFE JM, CONVERGENCE STEADY S

[9] Long-time behaviour of the solutions of one-dimensional nonlinear Hamilton-Jacobi equations [J].

Roquejoffre, JM .

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1998, 326 (02) :185-189

[10]

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