Min-max differential game with partial differential equation

Ebrahim. A. Youness; Abd El-Monem. A. Megahed; Elsayed. E. Eladdad; Hanem. F. A. Madkour; Ebrahim. A. Youness; Abd El-Monem. A. Megahed; Elsayed. E. Eladdad; Hanem. F. A. Madkour

doi:10.3934/math.2022759

AIMS Mathematics

2022, Volume 7, Issue 8: 13777-13789. doi: 10.3934/math.2022759

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Min-max differential game with partial differential equation

1.
Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
2.
Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismalia 41511, Egypt

Received: 03 January 2022 Revised: 01 May 2022 Accepted: 05 May 2022 Published: 23 May 2022
MSC : 35K15, 35A01, 35A02, 65M12, 91A05, 91A23

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.
- Cauchy initial value problem,
- min-max differential game,
- uniform convergence,
- existence,
- uniqueness,
- Picard method
Citation: Ebrahim. A. Youness, Abd El-Monem. A. Megahed, Elsayed. E. Eladdad, Hanem. F. A. Madkour. Min-max differential game with partial differential equation[J]. AIMS Mathematics, 2022, 7(8): 13777-13789. doi: 10.3934/math.2022759

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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.

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