Approximation of an optimal control problem governed by a differential parabolic inclusion

Abstract

In this article, we investigate the optimal control problem governed by parabolic inclusion. We describe the Galerkin approximation and we demonstrate the existence of the strong condensation points of the set of solutions of approximate optimization problems. Each of these points is a solution of the initial optimization problem.

Keywords:

• optimal control
• variational inclusions
• multivalued maps
• Galerkin approximation

AMS Subject Classifications::

• 49J24
• 49J40
• 49M15

Acknowledgement

The authors would like to thank the referee for his valuable suggestions and comments.