Optimal Control Problem for Non-linear Degenerate Parabolic Variation Inequality: Solvability and Attainability Issues

Abstract

We investigate the optimal control problem with respect to coefficients of the degenerate parabolic variational inequality. Since problems of this type can have the Lavrentieff effect, we consider the optimal control problem in a class of so-called Hadmissible solutions. We substantiate the attainability of H-optimal pairs via optimal solutions of some nondegenerate perturbed optimal control problems.

Keywords

• parabolic variation inequality
• optimal control problem
• control in coefficients
• approximation
• existence result
• attainability result