Abstract
Extremal problems for infinite order parabolic systems with time-varying lags are presented. An optimal boundary control problem for infinite order parabolic systems in which time-varying lags appear in the state equations and in the boundary conditions simultaneously is solved. The time horizon is fixed. Making use of Dubovicki-Milutin scheme, necessary and sufficient conditions of optimality for the Neumann problem with quadratic performance functionals and constrained control are derived.
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