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On the well-posedness and regularity of the waveequation with variable coefficients

Published online by Cambridge University Press:  05 September 2007

Bao-Zhu Guo  and
Zhi-Xiong Zhang
Bao-Zhu Guo
Affiliation:
Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100080, P.R. China; bzguo@iss.ac.cn School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa.
Zhi-Xiong Zhang
Affiliation:
Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100080, P.R. China; bzguo@iss.ac.cn Graduate University of Chinese Academy of Sciences, Beijing 100049, P.R. China.
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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.

Keywords

Wave equationtransfer functionwell-posed and regular systemboundary control and observation.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 4 , October 2007 , pp. 776 - 792
Copyright
© EDP Sciences, SMAI, 2007

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