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Analysis Of Singularities For Partial Differential Equations : Series In Applied And Computational Mathematics - Shuxing Chen

Analysis Of Singularities For Partial Differential Equations

Series In Applied And Computational Mathematics


Published: 31st December 2010
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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.

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"

Prefacep. v
Introduction to problems on singularity analysisp. 1
The classical singularity propagation theoremp. 1
Towards to modern theoryp. 9
Singularity analysis for linear equationsp. 13
Wave front setp. 13
Singularity propagation theorem for equations of principal typep. 23
Reflection of singularity on boundaryp. 30
Further discussionsp. 43
Generalized reflection of singularity on boundaryp. 43
The operators with multiple characteristicsp. 46
Singularity analysis for semilinear equationsp. 49
Theorem of propagation of 2s weak singularityp. 50
Theorem on propagation of 3s weak singularityp. 57
Singularity interaction and singularity indexp. 62
Propagation of conormal singularityp. 73
Interaction of conormal singularitiesp. 80
Extension of the concept of conormal singularitiesp. 80
Pseudo-compositionp. 86
Theorem on interaction of conormal singularitiesp. 87
Reflection of conormal singularitiesp. 90
Propagation of singularities for fully nonlinear equationsp. 93
Theorem of propagation of singularities for principal type equationsp. 93
Propagation of conormal singularities for nonlinear equationsp. 101
Propagation of strong singularities for nonlinear equationsp. 111
Solutions with fan-shaped singularity structure of semilinear equationsp. 112
Solutions with flower-shaped singularity structure of semilinear equationsp. 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 structurep. 137
Flower-shaped singularity structurep. 142
Formation of shocks for quasilinear hyperbolic equationsp. 147
The case of scalar equationp. 147
Two mechanism of blow-up of smooth solutionsp. 147
Formation of a shockp. 149
Estimates of the solution in the neighborhood of the starting point of shockp. 156
The case of systemp. 159
Background and conclusionp. 160
The property of the first approximate solutionp. 163
Estimates and convergence of the sequence of approximate solutionsp. 169
The case for full Euler systemp. 177
Brief review on paradifferential operatorsp. 181
Diadic decompositionp. 181
Paradifferential operators and paralinearzationp. 185
Paracompositionp. 189
Bibliographyp. 191
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9789814304832
ISBN-10: 9814304832
Series: Series In Applied And Computational Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 208
Published: 31st December 2010
Publisher: World Scientific Publishing Co Pte Ltd
Country of Publication: SG
Dimensions (cm): 22.86 x 15.24  x 1.91
Weight (kg): 0.5