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Serag, H.M., EL-Zahaby, S.A. and Abd Elrhman, L.M. (2015) Distributed Control for Cooperative Parabolic Systems with Conjugation Conditions. Journal of Progressive Research in Mathematics, 4, 348-365.

has been cited by the following article:

• TITLE: Boundary Control for Cooperative Elliptic Systems under Conjugation Conditions

  AUTHORS: H. M. Serag, L. M. Abd-Elrhman, A. A. Alsaban

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

  JOURNAL NAME: Advances in Pure Mathematics, Vol.11 No.5, May 25, 2021

  ABSTRACT: 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.