Mixed Optimal Control Vector for a Boundary Value Problem  of Couple Nonlinear Elliptic Equations

Safaa Juma  Al-Qaisi; Ghufran M  Kadhem; Jamil Amir   Al-Hawasy

doi:10.24996/ijs.2022.63.9.18

Authors

Safaa Juma Al-Qaisi Diyala Directorate of Education, Diyala-Iraq
Ghufran M Kadhem Babylonian Directorate of Education, Babylon-Iraq
Jamil Amir Al-Hawasy Department of Mathematics, College of Science, Mustansiriyah University, Baghdad-Iraq https://orcid.org/0000-0002-7225-8030

DOI:

https://doi.org/10.24996/ijs.2022.63.9.18

Keywords:

State Vector Solution, Mixed Optimal Control Vector, Couple Nonlinear Elliptic Boundary Value Problem

Abstract

In this research, we study the classical continuous Mixed optimal control vector problem dominated by couple nonlinear elliptic PDEs. The existence theorem for the unique state vector solution of the considered couple nonlinear elliptic PDEs for a given continuous classical mixed control vector is stated and proved by applying the Minty-Browder theorem under suitable conditions. Under suitable conditions, the existence theorem of a classical continuous mixed optimal control vector associated with the considered couple nonlinear elliptic PDEs is stated and proved.