Boundary feedback stabilization and Riesz basis property of a 1-d first order hyperbolic linear system with L∞-coefficients

被引：12

作者：

Chentouf, Boumediene ^{[1
]}

Wang, Jun-Min ^{[2
]}

机构：

[1] Sultan Qaboos Univ, Dept Math & Stat, Muscat 123, Oman

[2] Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2009年 / 246卷 / 03期

基金：

中国国家自然科学基金;

关键词：

First order hyperbolic linear system; L-infinity-coefficients; Regularization method; C-0-semigroup; Stability; Riesz basis; HEAT-EXCHANGER EQUATIONS; DISCONTINUOUS COEFFICIENTS; DIFFERENTIAL-EQUATIONS; EXPONENTIAL STABILITY; EXACT OBSERVABILITY; QUESTIONS; CONTROLLABILITY; REACHABILITY; UNIQUENESS; EXPANSION;

D O I：

10.1016/j.jde.2008.08.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：1119 / 1138

页数：20

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