On the controllability of the Laplace equation observed on an interior curve.

Título inglés	On the controllability of the Laplace equation observed on an interior curve.
Título español	Controlabilidad de la ecuación de Laplace observada en una curva interior.
Autor/es	Osses, A. ; Puel, J.-P.
Organización	Cent. Math. Appl. Ec. Polytechn., París, Francia;Univ. Versailles Saint-Quentin, París, Francia
Revista	1139-1138
Publicación	1998, 11 (2): 403-441, 25 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	The boundary approximate controllability of the Laplace equation observed on an interior curve is studied in this paper. First we consider the Laplace equation with a bounded potential. The Lp (1 < p < ∞) approximate controllability is established and controls of Lp-minimal norm are built by duality. At this point, a general result which clarifies the relationship between this duality approach and the classical optimal control theory is given. The results are extended to the Lp (1≤ p < ∞) approximate controllability with quasi bang-bang controls and finally to the semilinear case with a globally Lipschitz non linearity by a fixed point method. A counterexample shows that the globally Lipschitz hypothesis is essential. To compute the control, a numerical method based in the duality technique is proposed. It is tested in several cases obtaining a fast behavior in the case of fixed geometry.
Clasificación UNESCO	120204 ; 120702
Palabras clave español	Ecuación de Laplace ; Control óptimo ; Curvas ; Dualidad
Código MathReviews	MR1666505
Código Z-Math	Zbl 0919.35019
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