On the well-posedness and regularity of the wave equation with variable coefficients

Bao-Zhu Guo; Zhi-Xiong Zhang

ESAIM: Control, Optimisation and Calculus of Variations (2007)

  • Volume: 13, Issue: 4, page 776-792
  • ISSN: 1292-8119

Abstract

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An open-loop system of a multidimensional wave equation with variable coefficients, partial boundary Dirichlet control and collocated observation is considered. It is shown that the system is well-posed in the sense of D. Salamon and regular in the sense of G. Weiss. The Riemannian geometry method is used in the proof of regularity and the feedthrough operator is explicitly computed.

How to cite

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Guo, Bao-Zhu, and Zhang, Zhi-Xiong. "On the well-posedness and regularity of the wave equation with variable coefficients." ESAIM: Control, Optimisation and Calculus of Variations 13.4 (2007): 776-792. <http://eudml.org/doc/249986>.

@article{Guo2007,
abstract = { An open-loop system of a multidimensional wave equation with variable coefficients, partial boundary Dirichlet control and collocated observation is considered. It is shown that the system is well-posed in the sense of D. Salamon and regular in the sense of G. Weiss. The Riemannian geometry method is used in the proof of regularity and the feedthrough operator is explicitly computed. },
author = {Guo, Bao-Zhu, Zhang, Zhi-Xiong},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Wave equation; transfer function; well-posed and regular system; boundary control and observation.; boundary control and observation; multiplier method},
language = {eng},
month = {9},
number = {4},
pages = {776-792},
publisher = {EDP Sciences},
title = {On the well-posedness and regularity of the wave equation with variable coefficients},
url = {http://eudml.org/doc/249986},
volume = {13},
year = {2007},
}

TY - JOUR
AU - Guo, Bao-Zhu
AU - Zhang, Zhi-Xiong
TI - On the well-posedness and regularity of the wave equation with variable coefficients
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/9//
PB - EDP Sciences
VL - 13
IS - 4
SP - 776
EP - 792
AB - An open-loop system of a multidimensional wave equation with variable coefficients, partial boundary Dirichlet control and collocated observation is considered. It is shown that the system is well-posed in the sense of D. Salamon and regular in the sense of G. Weiss. The Riemannian geometry method is used in the proof of regularity and the feedthrough operator is explicitly computed.
LA - eng
KW - Wave equation; transfer function; well-posed and regular system; boundary control and observation.; boundary control and observation; multiplier method
UR - http://eudml.org/doc/249986
ER -

References

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