Exact controllability of the wave equation with mixed boundary condition and time-dependent coefficients

M. M. Cavalcanti

Archivum Mathematicum (1999)

  • Volume: 035, Issue: 1, page 29-57
  • ISSN: 0044-8753

Abstract

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In this paper we study the boundary exact controllability for the equation ∂ ∂ t α ( t ) ∂ y ∂ t - ∑ j = 1 n ∂ ∂ x j β ( t ) a ( x ) ∂ y ∂ x j = 0 in Ω × ( 0 , T ) , when the control action is of Dirichlet-Neumann form and Ω is a bounded domain in R n . The result is obtained by applying the HUM (Hilbert Uniqueness Method) due to J. L. Lions.

How to cite

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Cavalcanti, M. M.. "Exact controllability of the wave equation with mixed boundary condition and time-dependent coefficients." Archivum Mathematicum 035.1 (1999): 29-57. <http://eudml.org/doc/248369>.

@article{Cavalcanti1999,
abstract = {In this paper we study the boundary exact controllability for the equation \[ \frac\{\partial \}\{\partial t\}\left(\alpha (t)\{\{\partial y\}\over \{ \partial t\}\}\right)-\sum \_\{j=1\}^n\{\{\partial \}\over \{\partial x\_j\}\}\left(\beta (t)a(x)\{\{\partial y\}\over \{\partial x\_j\}\}\right)=0\;\;\;\hbox\{in\}\;\; \Omega \times (0,T)\,, \] when the control action is of Dirichlet-Neumann form and $\Omega $ is a bounded domain in $\{R\}^n$. The result is obtained by applying the HUM (Hilbert Uniqueness Method) due to J. L. Lions.},
author = {Cavalcanti, M. M.},
journal = {Archivum Mathematicum},
keywords = {wave equation; boundary value problem; exact controllability; Dirichlet-Neumann condition; wave equation; boundary value problem; exact controllability; Dirichlet-Neumann condition},
language = {eng},
number = {1},
pages = {29-57},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Exact controllability of the wave equation with mixed boundary condition and time-dependent coefficients},
url = {http://eudml.org/doc/248369},
volume = {035},
year = {1999},
}

TY - JOUR
AU - Cavalcanti, M. M.
TI - Exact controllability of the wave equation with mixed boundary condition and time-dependent coefficients
JO - Archivum Mathematicum
PY - 1999
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 035
IS - 1
SP - 29
EP - 57
AB - In this paper we study the boundary exact controllability for the equation \[ \frac{\partial }{\partial t}\left(\alpha (t){{\partial y}\over { \partial t}}\right)-\sum _{j=1}^n{{\partial }\over {\partial x_j}}\left(\beta (t)a(x){{\partial y}\over {\partial x_j}}\right)=0\;\;\;\hbox{in}\;\; \Omega \times (0,T)\,, \] when the control action is of Dirichlet-Neumann form and $\Omega $ is a bounded domain in ${R}^n$. The result is obtained by applying the HUM (Hilbert Uniqueness Method) due to J. L. Lions.
LA - eng
KW - wave equation; boundary value problem; exact controllability; Dirichlet-Neumann condition; wave equation; boundary value problem; exact controllability; Dirichlet-Neumann condition
UR - http://eudml.org/doc/248369
ER -

References

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  14. Lions J. L., Controlabilité Exacte, Perturbations et Stabilization de Systèmes Distribués, Tome 1, Masson, Paris, (1988). (1988) MR0953547

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