A Distributed Parabolic Control with Mixed Boundary Conditions

Authors

Jose-Luis Menaldi, Wayne State UniversityFollow
Domingo Alberto Tarzia, Universidad Austral

Document Type

Article

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 control ĝ_α with optimal state u_ĝαα and optimal adjoint state p_ĝαα are convergent as α → 1 (in norm of a suitable Sobolev parabolic space) to ĝ, u_ĝ and p_ĝ, 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.

Disciplines

Numerical Analysis and Computation | Probability

Comments

The final publication is available at IOS Press through http://content.iospress.com/articles/asymptotic-analysis/asy820

Recommended Citation

J.-L. Menaldi and D. A. Tarzia. A distributed parabolic control with mixed boundary conditions, Asyptotic Analysis 52 (2007), 227-241.