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Research Article | Open Access

Min-max differential game with partial differential equation

Ebrahim. A. Youness1, Abd El-Monem. A. Megahed2, Elsayed. E. Eladdad1, Hanem. F. A. Madkour1( )
Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismalia 41511, Egypt
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Abstract

In this paper, we are concerned with a min-max differential game with Cauchy initial value problem (CIVP) as the state trajectory for the differential game, we studied the analytical solution and the approximate solution by using Picard method (PM) of this problem. We obtained the equivalent integral equation to the CIVP. Also, we suggested a method for solving this problem. The existence, uniqueness of the solution and the uniform convergence are discussed for the two methods.

Keywords

Cauchy initial value problemmin-max differential gameuniform convergenceexistenceuniquenessPicard method
CLC number: 35K15, 35A01, 35A02, 65M12, 91A05, 91A23

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AIMS Mathematics
Volume 7 Issue 8,
August 2022
Pages 13777-13789
DOI: 10.3934/math.2022759

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Cite this article:
Youness EA, Megahed AE-MA, Eladdad EE, et al. Min-max differential game with partial differential equation. AIMS Mathematics, 2022, 7(8): 13777-13789. https://doi.org/10.3934/math.2022759

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Received: 03 January 2022
Revised: 01 May 2022
Accepted: 05 May 2022
Published: 15 August 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)