INV SUPERIOR JUBILADO
TARZIA domingo alberto
artículos
Título:
A distributed parabolic control with mixed boundary conditions
Autor/es:
J.L. MENALDI D.A. TARZIA
Revista:
ASYMPTOTIC ANALYSIS
Editorial:
IOS Press
Referencias:
Año: 2007 vol. 52 p. 227 - 241
ISSN:
0921-7134
Resumen:
We study the asymptotic behavior of an optimal distributed control
problem where the state is given by the heat equation with mixed
boundary conditions. The parameter $alpha$ intervenes in the Robin
boundary condition and it represents the heat transfer coefficient
on a portion $Gamma_1$ of the boundary of a given regular
$n$-dimensional domain. For each $alpha,$ the distributed
parabolic control problem optimizes the internal energy $g.$ It is
proven that the optimal control $hat{g}_{alpha}$ with optimal
state $u_{hat{g}_alphaalpha}$ and optimal adjoint state
$p_{hat{g}_{alpha}alpha}$ are convergent as $alpha oinfty$
(in norm of a suitable Sobolev parabolic space) to $hat{g},$
$u_{hat{g}}$ and $p_{hat{g}},$ respectively, where the limit
problem has Dirichlet (instead of Robin) boundary conditions on
$Gamma_1.$ The main techniques used are derived from the parabolic
variational inequality theory.