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Sobolev Spaces and Elliptic Boundary Value Problems Read chapter Read first chapter

2022 | OriginalPaper | Chapter

A Spectral Numerical Method to Approximate the Boundary Controllability of the Wave Equation with Variable Coefficients

Author : Carlos Castro

Published in: Research in PDEs and Related Fields

Publisher: Springer International Publishing

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Abstract

We present a spectral numerical method to approximate the boundary control of the wave equation with a non-constant potential. The numerical implementation is described and some numerical experiments show the efficiency of the method.

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previous chapter Survey on the Decay of the Local Energy for the Solutions of the Nonlinear Wave Equation
next chapter Aggregation Equation and Collapse to Singular Measure
Literature
1.
M. Abdelli, C. Castro, Numerical approximation of the averaged controllability for the wave equation with unknown velocity of propagation. ESAIM COCV 27(61) (2021)
2.
C. Castro, S. Micu, Boundary controllability of a linear semi-discrete 1-D wave equation derived from a mixed finite element method. Numer. Math. 102, 413–462 (2006)MathSciNetCrossRefMATH
3.
C. Castro, S. Micu, Uniform boundary observability of a linear semi-discrete 1-D wave equation with variable coefficients derived from a mixed finite element method, preprint
4.
C. Castro, S. Micu, A. Münch, Numerical approximation of the boundary control for the wave equation with mixed finite elements in a square. IMA J. Numer. Anal. 28, 186–214 (2008)MathSciNetCrossRefMATH
5.
S. Ervedoza, E. Zuazua, A systematic method for building smooth controls for smooth data. Discrete Contin. Dynam. Systems Series B 14, 1375–1401 (2010)MathSciNetCrossRefMATH
6.
S. Ervedoza, E. Zuazua Numerical Approximation of Exact Controls for Waves (Springer, Berlin, 2013)
7.
R. Glowinski, J.-L. Lions, Exact and approximate controllability for distributed parameter systems. Acta Numerica 3, 269–378 (1994)MathSciNetCrossRefMATH
8.
J.-L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Tome 1, in Recherches en Mathématiques Appliquées [Research in Applied Mathematics], Masson, Paris, vol. 8 (1988). Contrôlabilité exacte. [Exact controllability], With appendices by E. Zuazua, C. Bardos, G. Lebeau, J. Rauch
9.
P.-A. Raviart, J.-M. Thomas, Introduction l’analyse numrique des quations aux drives partielles (Dunod, Paris, 1998).
10.
E. Zuazua, Exact controllability for semilinear wave equations in one space dimension. Ann. de ’IHP, Section C 10(1), 109–129 (1993)
11.
E. Zuazua, Propagation, observation, and control of waves approximated by finite difference methods. SIAM Rev. 47(2), 197–243 (2005)MathSciNetCrossRefMATH
12.
C. Bardos, F. Bourquin, G. Lebeau, Calcul de dérivées normales et méthode de Galerkin appliqué au problème de contrôllabilité exacte. CR Acad. Sci. Paris 313(I), 757–760 (1991)MATH
13.
F. Bourquin, Approximation theory for the problem of exact controllability of the wave equation with boundary control. In: Second International Conference on Mathematical and Numerical Aspects of Wave Propagation (Newark, DE, 1993). SIAM, Philadelphia (1993) 103–112
Metadata
Title
A Spectral Numerical Method to Approximate the Boundary Controllability of the Wave Equation with Variable Coefficients
Author
Carlos Castro
Copyright Year
2022
Book
Research in PDEs and Related Fields

Print ISBN: 978-3-031-14267-3

Electronic ISBN: 978-3-031-14268-0

Copyright Year: 2022

DOI
https://doi.org/10.1007/978-3-031-14268-0_3