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 equation, transfer function, well-posed and regular system, boundary control and observation

@article{COCV_2007__13_4_776_0, author = {Guo, Bao-Zhu and Zhang, Zhi-Xiong}, title = {On the well-posedness and regularity of the wave equation with variable coefficients}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {776--792}, publisher = {EDP-Sciences}, volume = {13}, number = {4}, year = {2007}, doi = {10.1051/cocv:2007040}, mrnumber = {2351403}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2007040/} }

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 PY - 2007 SP - 776 EP - 792 VL - 13 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2007040/ DO - 10.1051/cocv:2007040 LA - en ID - COCV_2007__13_4_776_0 ER -

%0 Journal Article %A Guo, Bao-Zhu %A Zhang, Zhi-Xiong %T On the well-posedness and regularity of the wave equation with variable coefficients %J ESAIM: Control, Optimisation and Calculus of Variations %D 2007 %P 776-792 %V 13 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2007040/ %R 10.1051/cocv:2007040 %G en %F COCV_2007__13_4_776_0

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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