On the well-posedness and regularity of the wave equation with variable coefficients
ESAIM: Control, Optimisation and Calculus of Variations, Volume 13 (2007) no. 4, pp. 776-792.

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.

DOI: 10.1051/cocv:2007040
Classification: 35J50, 93C20, 93C25
Keywords: wave equation, transfer function, well-posed and regular system, boundary control and observation
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Guo, Bao-Zhu; Zhang, Zhi-Xiong. On the well-posedness and regularity of the wave equation with variable coefficients. ESAIM: Control, Optimisation and Calculus of Variations, Volume 13 (2007) no. 4, pp. 776-792. doi : 10.1051/cocv:2007040. http://www.numdam.org/articles/10.1051/cocv:2007040/

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