EXACT CONTROLLABILITY FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS WITH VERTICAL CHARACTERISTICS

• Published in: Acta mathematica scientia Vol. 29; no. 4; pp. 980 - 990
• Main Authors: Tatsien, Li, Bopeng, Rao
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2009; School of Mathematical Sciences, Fudan University, Shanghai 200433, China%Institut de Recherche Mathematique Avancee,Universite Louis Pasteur de Strasbourg, 67084 Strasbourg, France
• Subjects: 35B37; 35L60; 93B05; exact controllability; local distributed control; quasilinear hyperbolic systems; switching controls; 双曲型; 拟线性双曲系统; 控制方程; 精确可控性; 精确能控性; 零特征值; 35B37; 35L60; local distributed control; 93B05; switching controls; quasilinear hyperbolic systems; exact controllability; local distributed con-trol
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(09)60082-5

We consider first order quasilinear hyperbolic systems with vertical characteristics. 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 exact controllability only by means of physically meaningfnl 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.