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Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems

  • Couverture cartonnée
  • 160 Nombre de pages
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This book developed from a series of lectures I gave at the Symposium on Nonlinear Microlocal Analysis held at Nanjing University ... Lire la suite
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Description

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.

Contenu

I. Nonlinear Microlocal Analysis.- II. Appearance of Nonlinear Singularities.- III. Conormal Singularities.- IV. Conormal Regularity after Nonlinear Interaction.- V. Regularity and Singularities in Problems on Domains with Boundary.- VI. Conormal Waves on Domains with Boundary.- Index of Notation.

Informations sur le produit

Titre: Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems
Auteur:
Code EAN: 9780817634490
ISBN: 0817634495
Format: Couverture cartonnée
Genre: Mathématique
nombre de pages: 160
Poids: 252g
Taille: H235mm x B155mm x T8mm
Année: 1989
Auflage: 1989

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