Boundary Control for 2 × 2 Elliptic Systems with Conjugation Conditions

Ahlam Hasan Qamlo, Bahaa Gaber Mohammed

Department of Mathematics, Faculty of Applied Sciences, Umm AL-Qura University, Makkah, KSA.
Department of Mathematics, Faculty of Science, Taibah University, Madina, KSA.

DOI: 10.4236/ica.2013.43032                

Abstract

In this paper, we consider 2 × 2 non-cooperative elliptic system involving Laplace operator defined on bounded, continuous and strictly Lipschitz domain of Rn. First we prove the existence and uniqueness for the state of the system under conjugation conditions; then we discuss the existence of the optimal control of boundary type with Neumann conditions, and we find the set of equations and inequalities that characterize it.

Keywords

Boundary Control; Elliptic Systems; Conjugation Conditions; Non-Cooperative Systems; Neumann Conditions

Conflicts of Interest

The authors declare no conflicts of interest.

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