Weak KAM Solutions of a Discrete-Time Hamilton-Jacobi Equation in a Minimax Framework
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 prob...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/769368 |
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| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |