Fuchsian Reduction: Applications to Geometry, Cosmology and Mathematical Physics (Progress in Nonlinear Differential Equations and Their Applications, 71)

Kichenassamy, Satyanad

ISBN 10: 0817643524 / ISBN 13: 9780817643522

Published by Birkhäuser, 2007

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Bibliographic Details

Title: Fuchsian Reduction: Applications to Geometry...

Publisher: Birkhäuser

Publication Date: 2007

Binding: Hardcover

Condition: New

About this title

Synopsis:

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.