03503nam a22005295i 4500 978-0-8176-4637-0 DE-He213 20260521092029.0 cr nn 008mamaa 100301s2007 xxu| s |||| 0|eng d 9780817646370 99780817646370 10.1007/978-0-8176-4637-0 doi 515.353 23 Kichenassamy, Satyanad. author. Fuchsian Reduction [electronic resource] : Applications to Geometry, Cosmology, and Mathematical Physics / by Satyanad Kichenassamy. Boston, MA : Birkhäuser Boston, 2007. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Progress in Nonlinear Differential Equations and Their Applications ; 71 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. MATHEMATICS. DIFFERENTIAL EQUATIONS, PARTIAL. GLOBAL DIFFERENTIAL GEOMETRY. MATHEMATICAL PHYSICS. ASTROPHYSICS. RELATIVITY (PHYSICS). MATHEMATICS. PARTIAL DIFFERENTIAL EQUATIONS. APPLICATIONS OF MATHEMATICS. DIFFERENTIAL GEOMETRY. MATHEMATICAL METHODS IN PHYSICS. EXTRATERRESTRIAL PHYSICS, SPACE SCIENCES. RELATIVITY AND COSMOLOGY. SpringerLink (Online service) Springer eBooks Printed edition: 9780817643522 Progress in Nonlinear Differential Equations and Their Applications ; 71 http://dx.doi.org/10.1007/978-0-8176-4637-0 Ver el texto completo en las instalaciones del CICY ZDB-2-SMA ddc ER 35668 35668 0 0 ddc 0 0 LE CICY CICY EL 2025-10-06 0 515.353 2025-10-06 08:44:37 2025-10-06 ER