Optimal Control for Parabolic Variational Inequalities

Consider the problem of maximizing a functional that depends on a control function $k(x,t)$ and on the solution $u(x,t)$ of a parabolic variational inequality with k appearing in the data. Necessary conditions are obtained for the maximizers $k_0 (x,t)$, and the structure of $k_0 $ is then analyzed. An application to the Stefan problem is given.