Optimality of Distributed Control for *n × n* Hyperbolic Systems with an Infinite Number of Variables

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In this paper, we study the existence of solutions for 2*l* order (*n ×* *n*) cooperative systems governed by Dirichlet and Neumann problems
involving hyperbolic operators with an infinite number of variables and with
variable coefficients. The necessary and sufficient conditions for optimality
of the distributed control with constraints are obtained and the set of
inequalities that defining the optimal control of these systems are also
obtained.

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