Asymptotic analysis of some control problems

Article type: Research Article

Authors: Arada, Nadir | El Fekih, Henda | Raymond, Jean‐Pierre

Affiliations: UMR CNRS MIP, Université Paul Sabatier, 31062 Toulouse cedex 4, France. | Ecole Nationale d'Ingénieurs de Tunis, LAMSIN, BP 37, 1002 Tunis‐Belvédère, Tunisie. | UMR CNRS MIP, Université Paul Sabatier, 31062 Toulouse cedex 4, France.

Abstract: We study Dirichlet boundary control problem for semilinear parabolic equations, with pointwise state constraints. By penalizing the Dirichlet boundary condition, we define a family of control problems with Robin boundary conditions. We study the asymptotic behavior of solutions of these penalized problems, when the penalty parameter tends to infinity. We also prove that optimality conditions for the Dirichlet boundary control problem can be obtained by passage to the limit in the optimality conditions of the penalized problem.

Keywords: Dirichlet boundary control, Robin boundary control, pointwise state constraints, semilinear parabolic equation

Journal: Asymptotic Analysis, vol. 24, no. 3-4, pp. 343-366, 2000