Overview
- The applications worked out in Part III may serve as prototypes for use in new applications
- Can be used as a textbook in graduate courses
- Problems and bibliographic notes are included
Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 71)
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Table of contents (13 chapters)
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Front Matter
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Introduction
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Front Matter
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Fuchsian Reduction
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Front Matter
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Theory of Fuchsian Partial Di?erential Equations
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Front Matter
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Background Results
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
From the reviews:
“Fuchsian reduction is an analytical method to represent solutions to non-linear PDEs near singularities … . The book under review provides a careful and instructive introduction into this method. … At the end of most of the chapters some problems are posed, which are solved in an appendix. In total this is a highly interesting book containing a lot of original ideas and which suggests new developments.” (R. Steinbauer, Monatshefte für Mathematik, Vol. 158 (3), November, 2009)
Authors and Affiliations
Bibliographic Information
Book Title: Fuchsian Reduction
Book Subtitle: Applications to Geometry, Cosmology and Mathematical Physics
Authors: Satyanad Kichenassamy
Series Title: Progress in Nonlinear Differential Equations and Their Applications
DOI: https://doi.org/10.1007/978-0-8176-4637-0
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Boston 2007
Hardcover ISBN: 978-0-8176-4352-2Published: 18 September 2007
eBook ISBN: 978-0-8176-4637-0Published: 14 September 2007
Series ISSN: 1421-1750
Series E-ISSN: 2374-0280
Edition Number: 1
Number of Pages: XV, 289
Topics: Geometry, Partial Differential Equations, Applications of Mathematics, Differential Geometry, Mathematical Methods in Physics, Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics)