Optimal control of coefficients in parabolic free boundary problems modeling laser ablation

Variational Modeling of Parabolic Free Boundary Problems

Optimal boundary control problems of retarded parabolic systems

Various optimal control problems of infinite dimensional systems with point and distributed delays were considered in [1], [2], [3], [5], [6], [7], [8], [9], [10] and [15]. In [15], optimal control problems for parabolic systems with Neumann boundary conditions involving constant time delays were considered. Such systems constitute in a linear approximation, a universal mathematical model for m...

Optimal Control Problems for Parabolic Hemivariational Inequalities with Boundary Conditions

In this paper, we study optimal control problems for parabolic hemivariational inequalities of dynamic elasticity and investigate the continuity of the solution mapping from the given initial value and control data to trajectories. We show the existence of an optimal control which minimizes the quadratic cost function and establish the necessary conditions of optimality of an optimal control fo...

Free Boundary Problems for Parabolic Equations

An address delivered at the Ann Arbor meeting of the American Mathematical Society on November 29, 1969, by invitation of the Committee to Select Hour Speakers for Western Sectional Meetings; received by the editors April 9,1969. AMS 1969 subject classifications. Primary 3562, 3578.

Adjoint-Based Optimal Control of Time-Dependent Free Boundary Problems

In this paper we show a simplified optimisation approach for free boundary problems in arbitrary space dimensions. This approach is mainly based on an extended operator splitting which allows a decoupling of the domain deformation and solving the remaining partial differential equation. First we give a short introduction to free boundary problems and the problems occurring in optimisation. Then...