Existence, Uniqueness, and Convergence of optimal control problems associated with Parabolic variational inequalities of the second kind - Université Claude Bernard Lyon 1 Accéder directement au contenu
Article Dans Une Revue Nonlinear Analysis: Real World Applications Année : 2011

Existence, Uniqueness, and Convergence of optimal control problems associated with Parabolic variational inequalities of the second kind

Résumé

Let $u_{g}$ the unique solution of a parabolic variational inequality of second kind, with a given $g$. Using a regularization method, we prove, for all $g_{1}$ and $g_{2}$, a monotony property between $\mu u_{g_{1}} + (1-\mu)u_{g_{2}}$ and $u_{\mu g_{1} + (1-\mu)g_{2}}$ for $\mu \in [0 , 1]$. This allowed us to prove the existence and uniqueness results to a family of optimal control problems over $g$ for each heat transfer coefficient $h>0$, associated to the Newton law, and of another optimal control problem associated to a Dirichlet boundary condition. We prove also , when $h\to +\infty$, the strong convergence 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 a Dirichlet boundary condition.
Fichier principal
Vignette du fichier
NONRW-MT-2011.pdf (195.73 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00863327 , version 1 (18-09-2013)

Identifiants

Citer

Mahdi Boukrouche, Domingo A. Tarzia. Existence, Uniqueness, and Convergence of optimal control problems associated with Parabolic variational inequalities of the second kind. Nonlinear Analysis: Real World Applications, 2011, 12 (4), pp.2211-2224. ⟨hal-00863327⟩
119 Consultations
244 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More