TY - JOUR
T1 - Boundary feedback stabilization and Riesz basis property of a 1-d first order hyperbolic linear system with L∞-coefficients
AU - Chentouf, Boumediène
AU - Wang, Jun Min
N1 - Funding Information:
The authors are grateful to the anonymous referee for his/her constructive criticism and valuable suggestions and for having mentioned to them Ref. [18]. The first author also acknowledges the support of Sultan Qaboos University.
Funding Information:
E-mail addresses: chentouf@squ.edu.om (B. Chentouf), wangjc@graduate.hku.hk (J.-M. Wang). 1 The research of the author was supported by Sultan Qaboos University. 2 The research of the author was supported by the National Natural Science Foundation of China and the Program for New Century Excellent Talents in University of China.
PY - 2009/2/1
Y1 - 2009/2/1
N2 - This paper deals with the boundary feedback stabilization problem of a wide class of linear first order hyperbolic systems with non-smooth coefficients. We propose static boundary inputs (actuators) which lead us to a closed loop system with non-smooth coefficients and non-homogeneous boundary conditions. Then, we prove the exponential stability of the closed loop system under suitable conditions on the coefficients and the feedback gains. The key idea of the proof is to combine the regularization techniques with the characteristics method. Furthermore, by the spectral analysis method, it is also shown that the closed loop system has a sequence of generalized eigenfunctions, which form a Riesz basis for the state space, and hence the spectrum-determined growth condition is deduced.
AB - This paper deals with the boundary feedback stabilization problem of a wide class of linear first order hyperbolic systems with non-smooth coefficients. We propose static boundary inputs (actuators) which lead us to a closed loop system with non-smooth coefficients and non-homogeneous boundary conditions. Then, we prove the exponential stability of the closed loop system under suitable conditions on the coefficients and the feedback gains. The key idea of the proof is to combine the regularization techniques with the characteristics method. Furthermore, by the spectral analysis method, it is also shown that the closed loop system has a sequence of generalized eigenfunctions, which form a Riesz basis for the state space, and hence the spectrum-determined growth condition is deduced.
KW - C-semigroup
KW - First order hyperbolic linear system
KW - L-coefficients
KW - Regularization method
KW - Riesz basis
KW - Stability
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U2 - 10.1016/j.jde.2008.08.010
DO - 10.1016/j.jde.2008.08.010
M3 - Article
AN - SCOPUS:55649120663
SN - 0022-0396
VL - 246
SP - 1119
EP - 1138
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 3
ER -