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.