INV SUPERIOR JUBILADO
TARZIA domingo alberto
artículos
Título:
Existence, Uniqueness, and Convergence of optimal control problems associated with Parabolic variational inequalities of the second kind
Autor/es:
M. BOUKROUCHE; D.A. TARZIA
Revista:
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Editorial:
PERGAMON-ELSEVIER SCIENCE LTD
Referencias:
Año: 2011 vol. 12 p. 2211 - 2224
ISSN:
1468-1218
Resumen:
Let $u_{g}$  the unique solution of a parabolic variational  inequality  of  second kind, corresponding to the external force  $g$ (see ef{eq1}). We prove,  for all two data $g_{1}$ and $g_{2}$,  using a regularization method, a monotony property  between the  convex combination of two solutions $u_{g_{1}}$ , $u_{g_{2}}$  and the solution  associated to the  convex combination of the two data $g_{1}$ , $g_{2}$. This result  allows us, to  establish the strict convexity, for  the  cost functional ( ef{e4.1}) associated to the optimal control  problem ( ef{P}), over the external force  $g$ associated to the Dirichlet boundary  condition ( ef{pbc1}), and  the strict convexity for  the  cost functional ( ef{Jh}) associated to a family of optimal control  problem ( ef{Ph}), over the external force  $g$ for each heat transfer coefficient  $h>0$, associated to the  Newton law ( ef{pbc3}).  We prove  the strong  convergence, when $h o +infty$, of the  optimal controls and states associated to this  family of optimal control problems with the  Newton law  to that of the optimal control problem associated to the Dirichlet boundary  condition.