Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems: 130 (Progress in Mathematics) - Softcover

Beals, Michael

Softcover

ISBN 10: 0817634495 ISBN 13: 9780817634490

Verlag: Springer, 2013

Über diesen Titel

Reseña del editor

This book developed from a series of lectures I gave at the Symposium on Nonlinear Microlocal Analysis held at Nanjing University in October. 1988. Its purpose is to give an overview of the use of microlocal analysis and commutators in the study of solutions to nonlinear wave equations. The weak singularities in the solutions to such equations behave up to a certain extent like those present in the linear case: they propagate along the null bicharacteristics of the operator. On the other hand. examples exhibiting singularities not present in the linear case can also be constructed. I have tried to present a crossection of both the regularity results and the singular examples. for problems on the interior of a domain and on domains with boundary. The main emphasis is on the case of more than one space dimen­ sion. since that case is treated in great detail in the paper of Rauch-Reed 159]. The results presented here have for the most part appeared elsewhere. and are the work of many authors. but a few new examples and proofs are given. I have attempted to indicate the essential ideas behind the arguments. so that only some of the results are proved in full detail. It is hoped that the central notions of the more technical proofs appearing in research papers will be illuminated by these simpler cases.

Reseña del editor

Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems presents the first expository overview of the use of microlocal analysis and commutator techniques in the study of solutions to nonlinear wave equations. In a clear, comprehensive manner the author synthesizes a variety of research results from the last ten years, providing detailed proofs and descriptions of the central ideas behind the arguments and includes a number of figures to illustrate the theory's geometric aspects. The linear theory of the microlocal propagation of singularities and regularity is briefly recalled to motivate the nonlinear study. Weak singularities which propagate along null bicharacteristics are analyzed, and examples which exhibit singularities not present in the linear case are constructed. A selection of recent results on problems on the interior of a domain and on domains with boundary is presented. The book will be an invaluable reference for active researchers in linear microlocal analysis, hyperbolic equations, pseudo-differential operators, and nonlinear wave equations. It should also make excellent supplemental reading for a second year graduate course in partial differential equations.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2013
• ISBN 10: 0817634495
• ISBN 13: 9780817634490
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 160