Abstract
In this paper we investigate an optimal control problem in coefficients for degenerate parabolic variational inequality. Since these types of problems can exhibit the Lavrentieff phenomenon and non-uniqueness of weak solutions, there several possible statements of such problems depending on the choice of the class of admissible solutions. Here we consider the optimal control problem in the so-called class of H-admissible solutions. Using the classical approach to parabolic variational inequalities, we show that the set of admissible pairs is not empty. We prove some topological properties of the set of H-admissible solutions and show that this set possesses some compactness properties with respect to the appropriate convergence in variable spaces. Using, the direct method in Calculus of variations, we prove the theorem on the existence of H-optimal solutions.
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