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

Published online by Cambridge University Press:  19 September 2011

Larissa V. Fardigola
Larissa V. Fardigola*
Affiliation:
Mathematical Division, Institute for Low Temperature Physics and Engineering, 47 Lenin Ave., 61103 Kharkiv, Ukraine. fardigola@ukr.net
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Abstract

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

Keywords

Wave equationhalf-axiscontrollability probleminfluence operatorFourier transformSobolev spaceMoore-Penrose inverse
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 3 , July 2012 , pp. 748 - 773
Copyright
© EDP Sciences, SMAI, 2011

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