An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of homogenizing spike variation. Results for problems with state constraints are also stated. Mathematics Subject Classification. 49K20, 35B27. Received August 7...

The talk concerns minimax control problems for linear multidimensional parabolic systems with distributed uncertain perturbations and control functions acting in the Dirichlet boundary conditions. The underlying parabolic control system is functioning under hard/pointwise constraints on control and state variables. The main goal is to design a feedback control regulator that ensures the require...

Let ug the unique solution of a parabolic variational inequality of second kind, with a given g. Using a regularization method, we prove, for all g1 and g2, a monotony property between μug1 + (1 − μ)ug2 and uμg1+(1−μ)g2 for μ ∈ [0, 1]. This allowed us to prove the existence and uniqueness results to a family of optimal control problems over g for each heat transfer coefficient h > 0, associated...

This work is devoted to the functional a posteriori error analysis of multiharmonic finite element approximations to some distributed time-periodic parabolic optimal control problems. We derive easily computable, guaranteed upper bounds for both the state and co-state errors and the cost functional.

We discuss an optimal control problem of laser surface hardening of steel which is governed by a dynamical system consisting of a semilinear parabolic equation and an ordinary differential equation with a non differentiable right hand side function f+. To avoid the numerical and analytic difficulties posed by f+, it is regularized using a monotone Heaviside function and the regularized problem ...

A class of Lagrange-Newton-SQP methods is investigated for optimal control problems governed by semilinear parabolic initial-boundary value problems. Distributed and boundary controls are given, restricted by pointwise upper and lower bounds. The convergence of the method is discussed in appropriate Banach spaces. Based on a weak second order suucient optimality condition for the reference solu...

In this paper we consider a posteriori error estimates for space-time finite element discretizations for optimal control of hyperbolic partial differential equations of second order. It is an extension of Meidner & Vexler (2007), where optimal control problems of parabolic equations are analyzed. The state equation is formulated as a first order system in time and a posteriori error estimates a...