In this paper, we consider an optimal control problem, which is governed by a linear parabolic equation and is subject to state constraints pointwise in time. Optimal order error estimates are developed for a space-time finite element discretization of this problem. Numerical examples confirm the theoretical results. As a byproduct of our analysis, we derive a new regularity result for the opti...

In this paper, time-optimal control problem for a liner n n  co-operative parabolic system involving Laplace operator is considered. This problem is, steering an initial state   0 y u  , with control so that an observation , u   y t hits a given target set in minimum time. First, the existence and uniqueness of solutions of such system under conditions on the coefficients are proved. Afte...

A class of nonlinear elliptic and parabolic optimal control problems with mixed control-state constraints is considered. Extending a method known for the control of ordinary differential equations to the case of PDEs, the Yosida-Hewitt theorem is applied to show that the Lagrange multipliers are functions of certain Lp-spaces. By bootstrapping arguments, under natural assumptions, optimal contr...

We extend the existing techniques to study semidiscrete adaptive finite element approximation schemes for a constrained optimal control problem governed by parabolic integrodifferential equations. The control problem involves time accumulation and the control constrain is given in an integral obstacle sense. We first prove the uniqueness and existence of the solution of this optimal control pro...

This paper studies the averaging problem for some fully nonlinear equations of degenerate parabolic type with a Hamiltonian not necessarily periodic in the fast variable. Our aim is to point out a sufficient condition on the Hamiltonian to pass to the limit in the starting equation. Also, we investigate when this condition is not completely fulfilled and discuss some examples concerning determi...

This paper considers some typical optimal control problems for a class of strongly nonlinear parabolic systems. After some necessary preparation, it is shown that the family of admissible trajectories is a weakly closed and weakly sequentially compact subset of a reflexive Banach space and that the set of attainable states at any given time is a weakly compact subset of a Hilbert space. Using t...

Research on multigrid methods for optimization problems is reviewed. Optimization problems include shape design, parameter optimization, and optimal control problems governed by partial differential equations of elliptic, parabolic, and hyperbolic type.

This paper presents a new observability estimate for parabolic equations in Ω × (0, T ), where Ω is a convex domain. The observation region is restricted over a product set of an open nonempty subset of Ω and a subset of positive measure in (0, T ). This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property for norm a...

Abstract. This paper presents a new observability estimate for parabolic equations in × (0, T ), where  is a convex domain. The observation region is restricted over a product set of an open nonempty subset of  and a subset of positive measure in (0, T ). This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property f...

This work is devoted to the multiharmonic analysis of parabolic optimal control problems in a time-periodic setting. In contrast to previous approaches, we include the cases of different control and observation domains, the observation in certain energy spaces and the presence of control constraints. In all these cases we propose a new preconditioned MinRes solver for the frequency domain equat...