In this paper the time-optimal boundary control problem is presented for a distributed infinite order parabolic system in which time lags appear in the integral form both in the state equation and in the boundary condition. Some specific properties of the optimal control are discussed.

We consider the tracking problem for parabolic systems with boundary control. Assuming that the reference signal is bounded and measurable, we prove various regularity results as well representation formulas for the optimal control and the optimal trajectory.

In this paper we, apply the classical control theory to a parabolic partial differential equation in a bounded domain with diffusivity-interior-boundary actuation. We first we study the existence of the solution of the parabolic partial differential equation, then we study the solution bound estimate which are used to prove the existence of the solution of the optimal control problem in a Banac...

We analyze a (possibly degenerate) second order mean field games system of partial differential equations. The distinguishing features of the model considered are (1) that it is not uniformly parabolic, including the first order case as a possibility, and (2) the coupling is a local operator on the density. As a result we look for weak, not smooth, solutions. Our main result is the existence an...

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In this paper, the optimal boundary control problem for distributed parabolic systems, involving second order operator with an infinite number of variables, in which constant lags appear in the integral form both in the state equations and in the boundary condition is considered. Some specific properties of the optimal control are discussed.

the aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. the state and co-state are approximated by the lowest order raviart-thomas mixed finite element spaces and the control is not discreted. optimal error estimates in l2 are established for the state...