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well-posed andregular system

ESAIM: Control, Optimisation and Calculus of Variations (1)

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On the well-posedness and regularity of the waveequation with variable coefficients
Bao-Zhu Guo, Zhi-Xiong Zhang
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 13 / Issue 4 / October 2007

Published online by Cambridge University Press:

05 September 2007, pp. 776-792

Print publication:

October 2007
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An open-loop system of a multidimensional wave equationwith variable coefficients, partial boundary Dirichlet control andcollocated observation is considered. It is shown that the system iswell-posed in the sense of D. Salamon and regular in the sense of G.Weiss. The Riemannian geometry method is used in the proof ofregularity and the feedthrough operator is explicitly computed.