On optimal control for cooperative system governed by heat equation with conjugation conditions

Lamia M. Abd-Elrhman; A. A.  Alsaban

doi:10.5269/bspm.75745

Lamia M. Abd-Elrhman Al-Azhar university
A. A. Alsaban

Abstract

The optimal control for 2 × 2 cooperative Dirichlet and Neumann parabolic systems with conjugation conditions is considered. First the existence and uniqueness of the state are proved; then the necessary and sufficient conditions for the control to be an optimal is obtained by a set of inequalities. Also we generalize these discussions to n × n cooperative parabolic systems with conjugation conditions. The control in our problems is of distributed type and is allowed to be in a Hilbert space.

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