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001 978-0-8176-4637-0
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007 cr nn 008mamaa
008 100301s2007 xxu| s |||| 0|eng d
020 _a9780817646370
_9978-0-8176-4637-0
024 7 _a10.1007/978-0-8176-4637-0
_2doi
040 _aISI Library, Kolkata
050 4 _aQA440-699
072 7 _aPBM
_2bicssc
072 7 _aMAT012000
_2bisacsh
072 7 _aPBM
_2thema
082 0 4 _a516
_223
100 1 _aKichenassamy, Satyanad.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aFuchsian Reduction
_h[electronic resource] :
_bApplications to Geometry, Cosmology, and Mathematical Physics /
_cby Satyanad Kichenassamy.
264 1 _aBoston, MA :
_bBirkhäuser Boston,
_c2007.
300 _aXV, 289 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProgress in Nonlinear Differential Equations and Their Applications,
_x1421-1750 ;
_v71
505 0 _aFuchsian 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.
520 _aFuchsian 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.
650 0 _aGeometry.
650 0 _aDifferential equations, partial.
650 0 _aMathematics.
650 0 _aGlobal differential geometry.
650 0 _aMathematical physics.
650 0 _aAstrophysics.
650 1 4 _aGeometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21006
650 2 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
650 2 4 _aApplications of Mathematics.
_0http://scigraph.springernature.com/things/product-market-codes/M13003
650 2 4 _aDifferential Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21022
650 2 4 _aMathematical Methods in Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19013
650 2 4 _aSpace Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics).
_0http://scigraph.springernature.com/things/product-market-codes/P22030
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817670740
776 0 8 _iPrinted edition:
_z9780817643522
830 0 _aProgress in Nonlinear Differential Equations and Their Applications,
_x1421-1750 ;
_v71
856 4 0 _uhttps://doi.org/10.1007/978-0-8176-4637-0
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c425420
_d425420