Fuchsian Reduction [electronic resource] : Applications to Geometry, Cosmology, and Mathematical Physics / by Satyanad Kichenassamy.
Contributor(s): SpringerLink (Online service)Material type: TextSeries: Progress in Nonlinear Differential Equations and Their Applications: 71Publisher: Boston, MA : Birkhäuser Boston, 2007Description: XV, 289 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780817646370Subject(s): Mathematics | Partial differential equations | Applied mathematics | Engineering mathematics | Geometry | Differential geometry | Physics | Space sciences | Mathematics | Geometry | Partial Differential Equations | Applications of Mathematics | Differential Geometry | Mathematical Methods in Physics | Extraterrestrial Physics, Space SciencesAdditional physical formats: Printed edition:: No titleDDC classification: 516 LOC classification: QA440-699Online resources: Click here to access online
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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.