Weak KAM Solutions of a Discrete-Time Hamilton-Jacobi Equation in a Minimax Framework
Author
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-07-10
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
The purpose of this paper is to study the existence of solutions of a Hamilton-Jacobi equation in a minimax discrete-time case and to show different characterizations for a real number called the critical value, which plays a central role in this work.
We study the behavior of solutions of this problem using tools of game theory to obtain a “fixed point” of the Lax operator associated, considering some facts of weak KAM theory to interpret these solutions as discrete viscosity solutions.
These solutions represent the optimal payoff of a zero-sum game of two players, with increasingly long time payoffs.
The developed techniques allow us to study the behavior of an infinite time game without using discount factors or average actions.
American Psychological Association (APA)
Toledo, Porfirio. 2013. Weak KAM Solutions of a Discrete-Time Hamilton-Jacobi Equation in a Minimax Framework. Discrete Dynamics in Nature and Society،Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-497334
Modern Language Association (MLA)
Toledo, Porfirio. Weak KAM Solutions of a Discrete-Time Hamilton-Jacobi Equation in a Minimax Framework. Discrete Dynamics in Nature and Society No. 2013 (2013), pp.1-12.
https://search.emarefa.net/detail/BIM-497334
American Medical Association (AMA)
Toledo, Porfirio. Weak KAM Solutions of a Discrete-Time Hamilton-Jacobi Equation in a Minimax Framework. Discrete Dynamics in Nature and Society. 2013. Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-497334
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-497334