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		Mahdi BOUKROUCHE,Domingo A. TARZIA.[en_title][J].Control Theory and Technology,2013,11(3):422~427.[Copy]

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MahdiBOUKROUCHE,DomingoA.TARZIA
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(Lyon University, UJM F-42023, CNRS UMR 5208, Institut Camille Jordan;Departamento de Matem´atica-CONICET, FCE, Austral University)

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Received:July 04, 2012Revised:January 05, 2013

基金项目:This work was partly supported by the Institut Camille Jordan ST-Etienne University for first author, and the projects Argentine ANPCyT PICTO Austral 2008 # 73 and SOARD-AFOSR (No. FA9550-10-1-0023) for the second author.

Convergence of optimal control problems governed by second kind parabolic variational inequalities

Mahdi BOUKROUCHE,Domingo A. TARZIA

(Lyon University, UJM F-42023, CNRS UMR 5208, Institut Camille Jordan;Departamento de Matem´atica-CONICET, FCE, Austral University)

Abstract:

We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. We prove the strong convergence of the optimal control and state systems associated to this family to a similar optimal control problem. This work solves the open problem left by the authors in IFIP TC7 CSMO2011.

Key words: Parabolic variational inequalities of the second kind Aubin compactness arguments Boundary control Convergence of optimal control problems Tresca boundary conditions, free boundary problems