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＜電子ブック＞
Fuchsian Reduction : Applications to Geometry, Cosmology and Mathematical Physics / by Satyanad Kichenassamy
(Progress in Nonlinear Differential Equations and Their Applications. ISSN:23740280 ; 71)

版	1st ed. 2007.
出版者	(Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser)
出版年	2007
本文言語	英語
大きさ	XV, 289 p : online resource
著者標目	*Kichenassamy, Satyanad author SpringerLink (Online service)
件　名	LCSH:Geometry LCSH:Differential equations LCSH:Mathematics LCSH:Geometry, Differential LCSH:Mathematical physics LCSH:Solar system FREE:Geometry FREE:Differential Equations FREE:Applications of Mathematics FREE:Differential Geometry FREE:Mathematical Methods in Physics FREE:Space Physics
一般注記	Fuchsian Reduction -- Formal Series -- General Reduction Methods -- Theory of Fuchsian Partial Di?erential Equations -- Convergent Series Solutions of Fuchsian Initial-Value Problems -- Fuchsian Initial-Value Problems in Sobolev Spaces -- Solution of Fuchsian Elliptic Boundary-Value Problems -- Applications -- Applications in Astronomy -- Applications in General Relativity -- Applications in Differential Geometry -- Applications to Nonlinear Waves -- Boundary Blowup for Nonlinear Elliptic Equations -- Background Results -- Distance Function and Hölder Spaces -- Nash–Moser Inverse Function Theorem 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 HTTP:URL=https://doi.org/10.1007/978-0-8176-4637-0

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