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Differential Games and Representation Formulas for Solutions of Hamilton-Jacobi-Isaacs Equations.

Author: L C Evans; P E Souganidis; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER.
Publisher: Ft. Belvoir Defense Technical Information Center MAR 1983.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
Recent work by the authors and others has demonstrated the connections between the dynamic programming approach for two-person, zero-sum differential games and the new notion of viscosity solutions of Hamilton-Jacobi PDE, (Partial Differential Equations). The basic idea is that the dynamic programming optimality conditions imply that the values of a two-person, zero-sum differential game are viscosity solutions of  Read more...
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Document Type: Book
All Authors / Contributors: L C Evans; P E Souganidis; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER.
OCLC Number: 227580725
Notes: Prepared in cooperation with Maryland Univ., College Park. Dept. of Mathematics and Alfred P. Sloan Foundation.
Description: 50 pages

Abstract:

Recent work by the authors and others has demonstrated the connections between the dynamic programming approach for two-person, zero-sum differential games and the new notion of viscosity solutions of Hamilton-Jacobi PDE, (Partial Differential Equations). The basic idea is that the dynamic programming optimality conditions imply that the values of a two-person, zero-sum differential game are viscosity solutions of appropriate PDE. This paper proves the above, when the values of the differential games are defined following Elliott-Kalton. This results in a great simplification in the statements and proofs, as the definitions are explicit and do not entail any kind of approximations. Moreover, as an application of the above results, the paper contains a representation formula for the solution of a fully nonlinear first-order PDE. This is then used to prove results about the level sets of solutions of Hamilton-Jacobi equations with homogeneous Hamiltonians. These results are also related to the theory of Huygen's principle and geometric optics.

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