A Distributed Parabolic Control with Mixed Boundary Conditions Recommended Citation A Distributed Parabolic Control with Mixed Boundary Conditions
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Jose-Luis Menaldi, Domingo Tarzia, J.-L Menaldi, D Tarzia, Jose-Luis Menaldi, Alberto Domingo, Tarzia
2007 Volume 52
Abstract
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 α intervenes in the Robin boundary condition and it represents the heat transfer coefficient on a portion Γ1 of the boundary of a given regular n-dimensional domain. For each α, the distributed parabolic control problem optimizes the internal energy g. It is proven that the optimal controî gα with optimal state u ˆ gαα and optimal adjoint state p ˆ gαα are convergent as α → ∞ (in norm of a suitable Sobolev parabolic space) tô g, u ˆ g and p ˆ g , respectively, where the limit problem has Dirichlet (instead of Robin) boundary conditions on Γ1. The main techniques used are derived from the parabolic variational inequality theory.
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