Controllability problems for the 1-D wave equation on a half-axis with the Dirichlet boundary control

Larissa V. Fardigola

ESAIM: Control, Optimisation and Calculus of Variations (2012)

  • Volume: 18, Issue: 3, page 748-773
  • ISSN: 1292-8119

Abstract

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In this paper necessary and sufficient conditions of L∞-controllability and approximate L∞-controllability are obtained for the control system wtt = wxx − q2w, w(0,t) = u(t), x > 0, t ∈ (0,T), where q ≥ 0, T > 0, u ∈ L∞(0,T) is a control. This system is considered in the Sobolev spaces.

How to cite

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Fardigola, Larissa V.. "Controllability problems for the 1-D wave equation on a half-axis with the Dirichlet boundary control." ESAIM: Control, Optimisation and Calculus of Variations 18.3 (2012): 748-773. <http://eudml.org/doc/277826>.

@article{Fardigola2012,
abstract = {In this paper necessary and sufficient conditions of L∞-controllability and approximate L∞-controllability are obtained for the control system wtt = wxx − q2w, w(0,t) = u(t), x > 0, t ∈ (0,T), where q ≥ 0, T > 0, u ∈ L∞(0,T) is a control. This system is considered in the Sobolev spaces. },
author = {Fardigola, Larissa V.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Wave equation; half-axis; controllability problem; influence operator; Fourier transform; Sobolev space; Moore-Penrose inverse; wave equation},
language = {eng},
month = {11},
number = {3},
pages = {748-773},
publisher = {EDP Sciences},
title = {Controllability problems for the 1-D wave equation on a half-axis with the Dirichlet boundary control},
url = {http://eudml.org/doc/277826},
volume = {18},
year = {2012},
}

TY - JOUR
AU - Fardigola, Larissa V.
TI - Controllability problems for the 1-D wave equation on a half-axis with the Dirichlet boundary control
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2012/11//
PB - EDP Sciences
VL - 18
IS - 3
SP - 748
EP - 773
AB - In this paper necessary and sufficient conditions of L∞-controllability and approximate L∞-controllability are obtained for the control system wtt = wxx − q2w, w(0,t) = u(t), x > 0, t ∈ (0,T), where q ≥ 0, T > 0, u ∈ L∞(0,T) is a control. This system is considered in the Sobolev spaces.
LA - eng
KW - Wave equation; half-axis; controllability problem; influence operator; Fourier transform; Sobolev space; Moore-Penrose inverse; wave equation
UR - http://eudml.org/doc/277826
ER -

References

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