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Shock Waves and Reaction-Diffusion Equations : Grundlehren der mathematischen Wissenschaften - Joel Smoller

Shock Waves and Reaction-Diffusion Equations

Grundlehren der mathematischen Wissenschaften

Hardcover Published: 14th October 1994
ISBN: 9780387942599
Number Of Pages: 634

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The purpose of this book is to make easily available the basics of the theory of hyperbolic conservation laws and the theory of systems of reaction-diffusion equations, including the generalized Morse theory as developed by Charles Conley. It presents the modern ideas in these fields in a way that is accessible to a wider audience than just mathematicians.
The book is divided into four main parts: linear theory, reaction-diffusion equations, shock-wave theory, and the Conley index. For the second edition numerous typographical errors and other mistakes have been corrected and a new chapter on recent results has been added. The new chapter contains discussions of the stability of traveling waves, symmetry-breaking bifurcations, compensated compactness, viscous profiles for shock waves, and general notions for construction traveling-wave solutions for systems of nonlinear equations.

Acknowledgment
Preface to the Second Edition
Preface to the First Edition
List of Frequently Used Symbols
Basic Linear Theoryp. 1
Ill-Posed Problemsp. 3
Characteristics and Initial-Value Problemsp. 13
The One-Dimensional Wave Equationp. 17
Uniqueness and Energy Integralsp. 26
Holmgren's Uniqueness Theoremp. 33
An Initial-Value Problem for a Hyperbolic Equationp. 39
Distribution Theoryp. 45
Second-Order Linear Elliptic Equationsp. 64
Second-Order Linear Parabolic Equationsp. 78
Reaction - Diffusion Equationsp. 91
Comparison Theorems and Monotonicity Methodsp. 93
Linearizationp. 106
Topological Methodsp. 126
Bifurcation Theoryp. 167
Systems of Reaction-Diffusion Equationsp. 192
The Theory of Shock Wavesp. 237
Discontinuous Solutions of Conservation Lawsp. 239
The Single Conservation Lawp. 265
The Riemann Problem for Systems of Conservation Lawsp. 306
Applications to Gas Dynamicsp. 337
The Glimm Difference Schemep. 368
Riemann Invariants, Entropy, and Uniquenessp. 391
Quasi-Linear Parabolic Systemsp. 426
The Conley Indexp. 445
The Conley Indexp. 447
Index Pairs and the Continuation Theoremp. 478
Travelling Wavesp. 507
Recent Resultsp. 553
Bibliographyp. 607
Author Indexp. 621
Subject Indexp. 625
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387942599
ISBN-10: 0387942599
Series: Grundlehren der mathematischen Wissenschaften
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 634
Published: 14th October 1994
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 3.81
Weight (kg): 1.09
Edition Number: 2
Edition Type: Revised