ANALY OF SINGUL FOR PARTI DIFFER ..(V1)

By: CHEN SHUXING

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Hardcover | 29 September 2010

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Hardcover
208 Pages

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22.86 x 15.24 x 1.27

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The book provides a comprehensive overview on the theory on analysis of singularities for partial differential equations (PDEs). It contains a summarization of the formation, development and main results on this topic. Some of the author's discoveries and original contributions are also included, such as the propagation of singularities of solutions to nonlinear equations, singularity index and formation of shocks.

Industry Reviews

The choice of the topics is very interesting and the whole book is nicely written. It is essentially addressed to researchers in PDEs. In fact, the proofs are quite concise, and the whole book assumes a knowledge of the pseudodifferential calculus. -- Mathematical Reviews "Mathematical Reviews"

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Preface	p. v
Introduction to problems on singularity analysis	p. 1
The classical singularity propagation theorem	p. 1
Towards to modern theory	p. 9
Singularity analysis for linear equations	p. 13
Wave front set	p. 13
Singularity propagation theorem for equations of principal type	p. 23
Reflection of singularity on boundary	p. 30
Further discussions	p. 43
Generalized reflection of singularity on boundary	p. 43
The operators with multiple characteristics	p. 46
Singularity analysis for semilinear equations	p. 49
Theorem of propagation of 2s weak singularity	p. 50
Theorem on propagation of 3s weak singularity	p. 57
Singularity interaction and singularity index	p. 62
Propagation of conormal singularity	p. 73
Interaction of conormal singularities	p. 80
Extension of the concept of conormal singularities	p. 80
Pseudo-composition	p. 86
Theorem on interaction of conormal singularities	p. 87
Reflection of conormal singularities	p. 90
Propagation of singularities for fully nonlinear equations	p. 93
Theorem of propagation of singularities for principal type equations	p. 93
Propagation of conormal singularities for nonlinear equations	p. 101
Propagation of strong singularities for nonlinear equations	p. 111
Solutions with fan-shaped singularity structure of semilinear equations	p. 112
Solutions with flower-shaped singularity structure of semilinear equations	p. 122
Solutions with strong singularities of quasilinear equations (1-d case)	p. 131
Solutions with strong singularities of quasilinear equations (m-d case)	p. 137
Fan-shaped singularity structure	p. 137
Flower-shaped singularity structure	p. 142
Formation of shocks for quasilinear hyperbolic equations	p. 147
The case of scalar equation	p. 147
Two mechanism of blow-up of smooth solutions	p. 147
Formation of a shock	p. 149
Estimates of the solution in the neighborhood of the starting point of shock	p. 156
The case of system	p. 159
Background and conclusion	p. 160
The property of the first approximate solution	p. 163
Estimates and convergence of the sequence of approximate solutions	p. 169
The case for full Euler system	p. 177
Brief review on paradifferential operators	p. 181
Diadic decomposition	p. 181
Paradifferential operators and paralinearzation	p. 185
Paracomposition	p. 189
Bibliography	p. 191
Table of Contents provided by Ingram. All Rights Reserved.

ANALY OF SINGUL FOR PARTI DIFFER ..(V1)

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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