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

Osses, A., and Puel, J.-P.. "On the controllability of the Laplace equation observed on an interior curve.." Revista Matemática Complutense 11.2 (1998): 403-441. <http://eudml.org/doc/44458>.

@article{Osses1998,
abstract = {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 &lt; p &lt; ∞) 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 &lt; ∞) 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.},
author = {Osses, A., Puel, J.-P.},
journal = {Revista Matemática Complutense},
keywords = {Ecuación de Laplace; Control óptimo; Curvas; Dualidad; boundary approximate controllability; duality approach; numerical method},
language = {eng},
number = {2},
pages = {403-441},
title = {On the controllability of the Laplace equation observed on an interior curve.},
url = {http://eudml.org/doc/44458},
volume = {11},
year = {1998},
}

TY - JOUR
AU - Osses, A.
AU - Puel, J.-P.
TI - On the controllability of the Laplace equation observed on an interior curve.
JO - Revista Matemática Complutense
PY - 1998
VL - 11
IS - 2
SP - 403
EP - 441
AB - 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 &lt; p &lt; ∞) 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 &lt; ∞) 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.
LA - eng
KW - Ecuación de Laplace; Control óptimo; Curvas; Dualidad; boundary approximate controllability; duality approach; numerical method
UR - http://eudml.org/doc/44458
ER -