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

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

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

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topGuo, 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 -

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