Optimal boundary control of parabolic system on doubly connected region in new space

摘要

The optimal boundary control of the system governed by parabolic partial differential equations on a doubly connected region in the new space advanced by Lions is discussed. It proves the necessary and sufficient conditions for a control to be optimal and obtains the optimality system consisting of partial differential equations and variational inequalities. And the application of penalty shifting method to the approximate solution of control problems for the system is researched.