Global exact controllability for quasilinear hyperbolic systems of diagonal form with linearly degenerate characteristics

被引：10

作者：

Wang, Zhiqiang ^{[1
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 69卷 / 02期

基金：

中国国家自然科学基金;

关键词：

quasilinear hyperbolic system; linearly degenerate characteristic; initial-boundary value problem; global exact controllability;

D O I：

10.1016/j.na.2007.05.037

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the global exact controllability for first-order quasilinear hyperbolic systems of diagonal form with linearly degenerate characteristics. When the system has no zero characteristics, we establish the global exact boundary controllability from one arbitrarily preassigned Cl data to another by means of a constructive method, in which the desired boundary controls can be acted either on both sides or only on one side. Sharp estimates on the exact controllable time are given in both cases. When the system has some zero characteristics, the global exact controllability is also established. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：510 / 522

页数：13

共 12 条

[1] FORMATION OF SINGULARITIES IN ONE-DIMENSIONAL NONLINEAR-WAVE PROPAGATION [J].

JOHN, F .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1974, 27 (03) :377-405

[2] DEVELOPMENT OF SINGULARITIES OF SOLUTIONS OF NONLINEAR HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS [J].

LAX, PD .

JOURNAL OF MATHEMATICAL PHYSICS, 1964, 5 (05) :611-&

[3]

LI T. T., 1994, Research in Applied Mathematics, V32

[4]

Li T, 2007, COMMUN PUR APPL ANAL, V6, P229

[5]

Li T, 2007, INT J DYN SYST DIFFE, V1, P12, DOI 10.1504/IJDSDE.2007.013741

[6] Exact controllability for first order quasilinear hyperbolic systems with zero eigenvalues [J].

Li, TS ;

Yu, LX .

CHINESE ANNALS OF MATHEMATICS SERIES B, 2003, 24 (04) :415-422

[7] Global exact controllability of a class of quasilinear hyperbolic systems [J].

Li, TS ;

Zhang, BY .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 225 (01) :289-311

[8] Local exact boundary controllability for a class of quasilinear hyperbolic systems [J].

Li, TT ;

Rao, BP .

CHINESE ANNALS OF MATHEMATICS SERIES B, 2002, 23 (02) :209-218

[9] Exact boundary controllability for quasi-linear hyperbolic systems [J].

Li, TT ;

Rao, BP .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2003, 41 (06) :1748-1755

[10] The mixed initial-boundary value problem for reducible quasilinear hyperbolic systems with linearly degenerate characteristics [J].

Li, TT ;

Peng, YJ .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 52 (02) :573-583

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