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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832567657845489664 |
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| author | Porfirio Toledo |
| author_facet | Porfirio Toledo |
| author_sort | Porfirio Toledo |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-81c970fc0dac421fac6886413bdae6dc |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-81c970fc0dac421fac6886413bdae6dc2025-02-03T01:00:50ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/769368769368Weak KAM Solutions of a Discrete-Time Hamilton-Jacobi Equation in a Minimax FrameworkPorfirio Toledo0Facultad de Matemáticas, UV Zona Universitaria, 91090 Xalapa, Ver, MexicoThe 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.http://dx.doi.org/10.1155/2013/769368 |
| spellingShingle | Porfirio Toledo Weak KAM Solutions of a Discrete-Time Hamilton-Jacobi Equation in a Minimax Framework Discrete Dynamics in Nature and Society |
| title | Weak KAM Solutions of a Discrete-Time Hamilton-Jacobi Equation in a Minimax Framework |
| title_full | Weak KAM Solutions of a Discrete-Time Hamilton-Jacobi Equation in a Minimax Framework |
| title_fullStr | Weak KAM Solutions of a Discrete-Time Hamilton-Jacobi Equation in a Minimax Framework |
| title_full_unstemmed | Weak KAM Solutions of a Discrete-Time Hamilton-Jacobi Equation in a Minimax Framework |
| title_short | Weak KAM Solutions of a Discrete-Time Hamilton-Jacobi Equation in a Minimax Framework |
| title_sort | weak kam solutions of a discrete time hamilton jacobi equation in a minimax framework |
| url | http://dx.doi.org/10.1155/2013/769368 |
| work_keys_str_mv | AT porfiriotoledo weakkamsolutionsofadiscretetimehamiltonjacobiequationinaminimaxframework |