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Fuchsian Reduction

Applications to Geometry, Cosmology, and Mathematical Physics

  • Satyanad Kichenassamy

Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 71)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Satyanad Kichenassamy
      Pages 1-19
  3. Fuchsian Reduction

    1. Front Matter
      Pages 21-21
    2. Satyanad Kichenassamy
      Pages 23-43
    3. Satyanad Kichenassamy
      Pages 45-66
  4. Theory of Fuchsian Partial Di?erential Equations

    1. Front Matter
      Pages 67-67
    2. Satyanad Kichenassamy
      Pages 85-104
    3. Satyanad Kichenassamy
      Pages 105-118
  5. Applications

    1. Front Matter
      Pages 119-119
    2. Satyanad Kichenassamy
      Pages 121-127
    3. Satyanad Kichenassamy
      Pages 129-142
    4. Satyanad Kichenassamy
      Pages 143-162
    5. Satyanad Kichenassamy
      Pages 163-215
    6. Satyanad Kichenassamy
      Pages 217-228
  6. Background Results

    1. Front Matter
      Pages 229-229
    2. Satyanad Kichenassamy
      Pages 231-245
    3. Satyanad Kichenassamy
      Pages 247-275
  7. Back Matter
    Pages 277-289

About this book

Introduction

Fuchsian reduction is a method for representing solutions of nonlinear PDEs near singularities. The technique has multiple applications including soliton theory, Einstein's equations and cosmology, stellar models, laser collapse, conformal geometry and combustion. Developed in the 1990s for semilinear wave equations, Fuchsian reduction research has grown in response to those problems in pure and applied mathematics where numerical computations fail.

This work unfolds systematically in four parts, interweaving theory and applications. The case studies examined in Part III illustrate the impact of reduction techniques, and may serve as prototypes for future new applications. In the same spirit, most chapters include a problem section. Background results and solutions to selected problems close the volume.

This book can be used as a text in graduate courses in pure or applied analysis, or as a resource for researchers working with singularities in geometry and mathematical physics.

Keywords

Cosmology EFE Einstein's equation Relativity Sobolev space general relativity mathematical physics stellar wave equation

Authors and affiliations

  • Satyanad Kichenassamy
    • 1
  1. 1.Universiteé de Reims Champagne-ArdenneF-51687 Reims Cedex 2France

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4637-0
  • Copyright Information Birkhäuser Boston 2007
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4352-2
  • Online ISBN 978-0-8176-4637-0
  • Series Print ISSN 1421-1750
  • Series Online ISSN 2374-0280
  • Buy this book on publisher's site
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