Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON OPTIMAL CONTROL FOR COOPERATIVE ELLIPTIC SYSTEMS UNDER CONJUGATION CONDITIONS

  • H.M. SERAG (Department of Mathematics, Faculty of Science, Al-Azhar University) ;
  • L.M. ABD-ELRHMAN (Department of Mathematics, Faculty of Science, Al-Azhar University[for girls]) ;
  • A.A. AL-SABAN (Department of Mathematics, Faculty of Science, Ibb University)
  • Received : 2021.06.21
  • Accepted : 2023.02.09
  • Published : 2023.03.30
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Abstract

In this paper, we consider cooperative elliptic systems under conjugation conditions. We first prove the existence of the state for 2 × 2 cooperative elliptic systems with Dirichlet and Neumann conditions, then we find the set of equations and inequalities that characterizes the optimal control of distributed type for these systems. The case of n × n cooperative systems is also established.

Keywords

Acknowledgement

The authors would like to express their gratitude to Professor Dr. I. M. Gali, Mathematics Department, Faculty of Science, Al-Azhar University, for suggesting the problem and critically reading the manuscript.

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