EXACT CONTROLLABILITY FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS WITH VERTICAL CHARACTERISTICS

doi:10.1016/S0252-9602(09)60082-5

Acta mathematica scientia,Series B ›› 2009, Vol. 29 ›› Issue (4): 980-990.doi: 10.1016/S0252-9602(09)60082-5

• Articles • Previous Articles Next Articles

EXACT CONTROLLABILITY FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS WITH VERTICAL CHARACTERISTICS

LI Da-Qian, RAO Ba-Feng

School of Mathematical Sciences, Fudan University, Shanghai 200433, China|Institut de Recherche Mathèmatique Avancée, Université|Louis Pasteur de Strasbourg, 67084 Strasbourg, France

Received:2009-01-14 Online:2009-07-20 Published:2009-07-20

Abstract

Abstract:

We consider first order quasilinear hyperbolic systems with vertical charac-teristics. It was shown in [4] that such systems can be exactly controllable with the help of internal controls applied to the equations corresponding to zero eigenvalues. However, it is possible that, for physical or engineering reasons, we can not put any control on
the equations corresponding to zero eigenvalues. In this paper, we will establish the ex-act controllability only by means of physically meaningful internal controls applied to the equations corresponding to non-zero eigenvalues. We also show the exact controllability for a very simplified model by means of switching controls.

Key words: quasilinear hyperbolic systems, exact controllability, local distributed con-trol, switching controls

CLC Number:

93B05

LI Da-Qian, RAO Ba-Feng. EXACT CONTROLLABILITY FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS WITH VERTICAL CHARACTERISTICS[J].Acta mathematica scientia,Series B, 2009, 29(4): 980-990.

Trendmd

[1]	Sanjukta DAS, Dwijendra PANDEY, N. SUKAVANAM. EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY [J]. Acta mathematica scientia,Series B, 2016, 36(5): 1509-1523.
[2]	FU Xian-Long, ZHANG Yu. EXACT NULL CONTROLLABILITY OF NON-AUTONOMOUS FUNCTIONAL EVOLUTION SYSTEMS WITH NONLOCAL CONDITIONS [J]. Acta mathematica scientia,Series B, 2013, 33(3): 747-757.
[3]	Tujin Kim, CHANG Qian-Shun, XU Jing. NOTE ON AN OPEN PROBLEM OF HIGHER ORDER NONLINEAR EVOLUTION EQUATIONS [J]. Acta mathematica scientia,Series B, 2012, 32(6): 2369-2376.
[4]	XU You-Jun, LIU Zhen-Hai. CONTROLLABILITY FOR A PARABOLIC EQUATION WITH A NONLINEAR TERM INVOLVING THE STATE AND THE GRADIENT [J]. Acta mathematica scientia,Series B, 2010, 30(5): 1593-1604.
[5]	TAN Lian-Sheng. ON DETERMINATION OF THE IMPULSIVE SOLUTIONS AND IMPULSIVE PROPERTIES TO LINEAR NON-HOMOGENEOUS MATRIX DIFFERENTIAL EQUATIONS [J]. Acta mathematica scientia,Series B, 2000, 20(2): 261-272.

EXACT CONTROLLABILITY FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS WITH VERTICAL CHARACTERISTICS

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 5

Metrics

Comments

Recommended 0