Controllability and Observability for Quasilinear Hyperbolic Systems
By Tatsien Li
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.
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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.
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