Author(s)

H. M. Serag¹, L. M. Abd-Elrhman², A. A. Alsaban³

¹Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt.
²Department of Mathematics, Faculty of Science, Al-Azhar University [for Girls], Nasr City, Cairo, Egypt.
³Department of Mathematics, Faculty of Science, Ibb University, Ibb, Yemen.

The existence and uniqueness of the state for 2 × 2 Dirichlet cooperative elliptic systems under conjugation conditions are proved using Lax-Milgram lemma, then the boundary control for these systems is discussed. The set of equations and inequalities that characterizes this boundary control is found by theory of Lions, Sergienko and Deineka. The problem for cooperative Neumann elliptic systems under conjugation conditions is also considered. Finally, the problem for n × n cooperative elliptic systems under conjugation conditions is established.

Cooperative Systems, Conjugation Conditions, Dirichlet and Neumann Conditions, Existence and Uniqueness of Solutions, Boundary Control

Serag, H. , Abd-Elrhman, L. and Alsaban, A. (2021) Boundary Control for Cooperative Elliptic Systems under Conjugation Conditions. Advances in Pure Mathematics, 11, 457-471. doi: 10.4236/apm.2021.115032.