擬線性雙曲系統的能控性與能觀性

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The controllability and observability are of great importance in boththeory and applications. A complete theory has been established for linearhyperbolic systems, in particular, for linear wave equations. There havealso been some results for semilinear wave equations. For quasilinearhyperbolic systems that have numerous applications in mechanics, physicsand other applied sciences, however, very few results are available evenwith space dimension one.

This monograph is based mainly on the results obtained by the author andhis collaborators in recent years. By mea~~s of the theory on the semi-globalclassical solution, a simple and direct constructive method is presentedin a systematic way to get both the controllability and observability in theframework of classical solutions for general first order 1-D quasilinearhyperbolic systems with general nonlinear boundary conditions.Corresponding applications are given for 1-D quasilinear wave equationsand 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 especiallywritten for those readers who are not familiar with quasilinear hyperbolic systems.

This book will be of benefit to scholars and graduate students in appliedmathematics and applied sciences. It may be used as a textbook or a mainreference for graduate students in corresponding areas.~

擬線性雙曲系統的能控性與能觀性

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