Controllability and Observability for Quasilinear Hyperbolic Systems - Hardcover

Tatsien Li

Hardcover

ISBN 10: 7040241633 ISBN 13: 9787040241631

Publisher: American Institute of Mathematical Sciences, 2010

Synopsis

The controllability and observability are of great importance in both theory and applications. A complete theory has been established for linear hyperbolic systems, in particular, for linear wave equations. There have also been some results for semilinear wave equations. For quasilinear hyperbolic systems that have numerous applications in mechanics, physics and other applied sciences, however, very few results are available even with space dimension one. This monograph is based mainly on the results obtained by the author and his collaborators in recent years. By means of the theory on the semi-global classical solution, a simple and direct constructive method is presented in a systematic way to get both the controllability and observability in the framework of classical solutions for general first order 1-D quasilinear hyperbolic systems with general nonlinear boundary conditions. Corresponding applications are given for 1-D quasilinear wave equations and for unsteady flows in a tree-like network of open canals, respectively. More than one hundred related references are provided. This book with 11 chapters is self-contained. An appendix is especially written for those readers who are not familiar with quasilinear hyperbolic systems. This book will be of benefit to scholars and graduate students in applied mathematics and applied sciences. It may be used as a textbook or a main reference for graduate students in corresponding areas.

About this title

About the Author

Tatsien Li is Graduated from the Department of Mathematics, Fudan University in 1957. He is professor of Fudan University(1980-), member of the Chinese Academy of Sciences (1995-), fellow of the Academy of Sciences for the Developing World(1997-), foreign member of the French Academy of Sciences(2005-), member of the European Academy of Sciences(2007-) and foreign member of the Portuguese Academy of Sciences(2008-). Professor Li is now the Co-Director of the Institut Sino-Francais de Mathematiquees Appliquees(ISFMA) since 1998, the Honorary President of the China Society for Industrial and Applied Mathematics(CSIAM) since 2008 and the Officer-at-large of the International Council for Industrial and Applied mathematics(ICIAM) since 2003. He was a visiting scholar at College de France, Paris, France, from 1979 to 1981, the Dean of the Graduate School of Fudan University from 1991 to 1999, the Vice-President of the Chinese Mathematical Society from 1996 to 2003, the Vice-President of the Shanghai Association for Science and Technology from 1996 to 2006 and the President of the CSIAM from 2000 to 2008. Professor Li,whose research fields include partial defferential equations, control theory and their applications, has published more than 200 papers and 18 monograghs and textbooks.

Edition details

• Publisher: American Institute of Mathematical Sciences
• Publication date: 2010
• Language: English
• ISBN 10: 7040241633
• ISBN 13: 9787040241631
• Binding: Hardcover
• Edition number: 1
• Number of pages: 222
• Editor: Alberto Bressan, H. Mete Soner, Eitan Tadmor, Luigi Ambrosio, Peter S. Constantin