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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Differential games with Lipschitz control functions and applications to games with partial differential equations


Author: Emmanuel Nicholas Barron
Journal: Trans. Amer. Math. Soc. 219 (1976), 39-76
MSC: Primary 93C20; Secondary 90D25
DOI: https://doi.org/10.1090/S0002-9947-1976-0419010-4
MathSciNet review: 0419010
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Abstract: In §1 we formulate a differential game when the dynamics is the inhomogeneous heat equation. In §2 we state the basic theory of differential games when the controls must choose uniformly Lipschitz control functions. We then prove some general theorems for the case when the controls may choose any measurable control functions. These theorems hold for games with any dynamics. In §3 we apply our theory developed to our particular example and in §4 we prove the existence of value for games with partial differential equations.


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DOI: https://doi.org/10.1090/S0002-9947-1976-0419010-4
Keywords: Lipschitz differential game, differential games with partial differential equations, Isaacs' condition
Article copyright: © Copyright 1976 American Mathematical Society