Abstract
Various optimization problems for linear parabolic systems with multiple constant time delays are considered. In this paper, we consider an optimal distributed control problem for a linear infinite order parabolic system in which multiple constant time delays appear in the state equation. Sufficient conditions for the existence of a unique solution of the infinite order parabolic time delay equation with the Dirichlet boundary condition are proved. The time horizon T is fixed. Making use of the Lions scheme [6], necessary and sufficient conditions of optimality for the Dirichlet problem with the quadratic performance functional with pointwise observation of the state and constrained control are derived.
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