A Distributed Parabolic Control with Mixed Boundary Conditions Recommended Citation A Distributed Parabolic Control with Mixed Boundary Conditions release_edqwh6cwnratllw65qn6rndtaq

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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