Some new results related to the null controllability of the $1-d$ heat equation

López, Antonio, and Zuazua, Enrique. "Some new results related to the null controllability of the $1-d$ heat equation." Séminaire Équations aux dérivées partielles 1997-1998 (1997-1998): 1-22. <http://eudml.org/doc/10958>.

@article{López1997-1998,
abstract = {We address three null controllability problems related to the $1-d$ heat equation. First we show that the $1-d$ heat equation with a rapidly oscillating density is uniformly null controllable as the period of the density tends to zero. We also prove that the same result holds for the finite-difference semi-discretization in space of the constant coefficient heat equation as the step size tends to zero. Finally, we prove that the null controllability of the constant coefficient heat equation can be obtained as limit of null controllability properties for singularly perturbed dissipative wave equations. The proofs combine results on sums of real exponentials, Carleman’s inequalities for heat equations and sideways energy estimates for wave equations.},
affiliation = {Departamento de Matemática Aplicada, Universidad Complutense, 28040 Madrid. Spain; Departamento de Matemática Aplicada, Universidad Complutense, 28040 Madrid. Spain},
author = {López, Antonio, Zuazua, Enrique},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {1D heat equation; null-controllability; rapidly oscillating coefficients; singular perturbations; discretization},
language = {eng},
pages = {1-22},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Some new results related to the null controllability of the $1-d$ heat equation},
url = {http://eudml.org/doc/10958},
volume = {1997-1998},
year = {1997-1998},
}

TY - JOUR
AU - López, Antonio
AU - Zuazua, Enrique
TI - Some new results related to the null controllability of the $1-d$ heat equation
JO - Séminaire Équations aux dérivées partielles
PY - 1997-1998
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 1997-1998
SP - 1
EP - 22
AB - We address three null controllability problems related to the $1-d$ heat equation. First we show that the $1-d$ heat equation with a rapidly oscillating density is uniformly null controllable as the period of the density tends to zero. We also prove that the same result holds for the finite-difference semi-discretization in space of the constant coefficient heat equation as the step size tends to zero. Finally, we prove that the null controllability of the constant coefficient heat equation can be obtained as limit of null controllability properties for singularly perturbed dissipative wave equations. The proofs combine results on sums of real exponentials, Carleman’s inequalities for heat equations and sideways energy estimates for wave equations.
LA - eng
KW - 1D heat equation; null-controllability; rapidly oscillating coefficients; singular perturbations; discretization
UR - http://eudml.org/doc/10958
ER -