Fuchsian Reduction

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.

• Cosmology
• EFE
• Einstein's equation
• Relativity
• Sobolev space
• general relativity
• mathematical physics
• stellar
• wave equation
• partial differential equations

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)

• Universiteé de Reims Champagne-Ardenne, F-51687 Reims Cedex 2, France

  Satyanad Kichenassamy

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