Weak KAM theory for a weakly coupled system of Hamilton-Jacobi equations

被引：4

作者：

Figalli, Alessio ^{[1
]}

Gomes, Diogo ^{[2
]}

Marcon, Diego ^{[3
]}

机构：

[1] Univ Texas Austin, Dept Math, 1 Univ Stn,C1200, Austin, TX 78712 USA

[2] KAUST, CEMSE Div, Thuwal 239556900, Saudi Arabia

[3] Univ Fed Rio Grande do Sul, Inst Matemat & Estat, BR-91509900 Porto Alegre, RS, Brazil

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2016年 / 55卷 / 04期

关键词：

LARGE-TIME BEHAVIOR; DYNAMICAL-APPROACH;

D O I：

10.1007/s00526-016-1016-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Here, we extend the weak KAM and Aubry-Mather theories to optimal switching problems. We consider three issues: the analysis of the calculus of variations problem, the study of a generalized weak KAM theorem for solutions of weakly coupled systems of Hamilton-Jacobi equations, and the long-time behavior of time-dependent systems. We prove the existence and regularity of action minimizers, obtain necessary conditions for minimality, extend Fathi's weak KAM theorem, and describe the asymptotic limit of the generalized Lax-Oleinik semigroup.

引用

页数：32

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