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

Mahdi Boukrouche (1) , Domingo A. Tarzia (2)

1 ICJ - Institut Camille Jordan
2 FCP, Univ. Austral, Paraguay 1950, S2000FZF Rosario, Argentina.

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 controls 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.

Mots clés: Parabolic variational inequalities of the second kind; Aubin compactness arguments; Control border; Convergence of optimal control problems; Tresca boundary conditions; free boundary problems

Domaines: Equations aux dérivées partielles [math.AP]

Mahdi Boukrouche, Domingo A. Tarzia. Convergence of optimal control problems governed by second kind parabolic variational inequalities. J Control Theory Appl, 2013, 11 (3), pp.422-427. ⟨10.1007/s11768-013-2155-2⟩. ⟨hal-00863292⟩