OPTIMAL CONTROL OF DISTRIBUTED PARAMETER SYSTEM GIVEN BY CAHN-HILLIARD EQUATION

Abstract

In this work, optimal control problem is addressed for distributed systems describedby Cahn-Hilliard equation by the means of distributed control, initial control andNeumann boundary control. The existence and uniqueness is provided for weak solutionusing variational method. Further, existence of optimal control is proved completely, andoptimality conditions is established for integral cost and quadratic cost, respectively. Lastly,Bang-Bang principle is deduced.