Global Propagation of Regular Nonlinear Hyperbolic Waves
This book studies the global propagation of the regular nonlinear hyperbolic wavedescribedby?rst-orderquasilinearhyperbolicsystemsintheone-spa- dimensioned case. Via the concept of weak linear degeneracy and the method of (generalized) normalized coordinates, a systematic theory is established on the global existence and the blow-up mechanism of the regular nonlinear hyperbolic wave with small amplitude not only for the Cauchy problem, but also for some other important problems such as the Cauchy problem on a semibounded initial data, the one-sided mixed initial-boundary value pr- lem, the generalized Riemann problem, and the generalized nonlinear initi- boundary Riemann problem, etc, as well as not only for the direct problem, butalsoforinverseproblemssuchastheinversegeneralizedRiemannproblem and the inverse piston problem. Most of the material contained in this book is based on the results the authors obtained in recent years. Some material that was previously published has been revised and updated. Thewholeapproachinthisbookisbasedonthetheoryofthelocalregular solution and of the local piecewise regular solution for quasilinear hyperbolic systems. For more comprehensive information, the reader may refer to the book by Li Tatsien and Yu Wenci, Boundary Value Problems for Quasilinear Hyperbolic Systems (Duke University Mathematics Series V, 1985). The?rstauthorwouldliketotakethisopportunitytogivehiswarmthanks to Professor Gu Chaohao for having initiated and brought him into the fru- ful area of quasilinear hyperbolic systems. The authors are very grateful to all the members on the Applied PDEs Seminar of Fudan University, or- nized by Qin Tiehu, Zhou Yi, and the ?rst author, for their constant interest, discussion, and suggestion on the subject.
Provides a complete theory for waves with general system conditions and boundary conditionsFeatures many related applications to mechanics and physicsContains much material based on the results obtained by the authors is recent years