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121227s1997 gw | s |||| 0|eng d |
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|a 9783540695943
|9 978-3-540-69594-3
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|a 10.1007/BFb0092831
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|a 515.353
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|a neuberger, john.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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|a Sobolev Gradients and Differential Equations
|h [electronic resource] /
|c by john neuberger.
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|a 1st ed. 1997.
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|a Berlin, Heidelberg :
|b Springer Berlin Heidelberg :
|b Imprint: Springer,
|c 1997.
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|a VIII, 152 p.
|b online resource.
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|a text
|b txt
|2 rdacontent
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|a computer
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|a online resource
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|a text file
|b PDF
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 1670
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|a Several gradients -- Comparison of two gradients -- Continuous steepest descent in Hilbert space: Linear case -- Continuous steepest descent in Hilbert space: Nonlinear case -- Orthogonal projections, Adjoints and Laplacians -- Introducing boundary conditions -- Newton's method in the context of Sobolev gradients -- Finite difference setting: the inner product case -- Sobolev gradients for weak solutions: Function space case -- Sobolev gradients in non-inner product spaces: Introduction -- The superconductivity equations of Ginzburg-Landau -- Minimal surfaces -- Flow problems and non-inner product Sobolev spaces -- Foliations as a guide to boundary conditions -- Some related iterative methods for differential equations -- A related analytic iteration method -- Steepest descent for conservation equations -- A sample computer code with notes.
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|a A Sobolev gradient of a real-valued functional is a gradient of that functional taken relative to the underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. Equal emphasis is placed on numerical and theoretical matters. Several concrete applications are made to illustrate the method. These applications include (1) Ginzburg-Landau functionals of superconductivity, (2) problems of transonic flow in which type depends locally on nonlinearities, and (3) minimal surface problems. Sobolev gradient constructions rely on a study of orthogonal projections onto graphs of closed densely defined linear transformations from one Hilbert space to another. These developments use work of Weyl, von Neumann and Beurling.
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|a Partial differential equations.
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|a Numerical analysis.
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|a Partial Differential Equations.
|0 http://scigraph.springernature.com/things/product-market-codes/M12155
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|a Numerical Analysis.
|0 http://scigraph.springernature.com/things/product-market-codes/M14050
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9783662182192
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|i Printed edition:
|z 9783540635376
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 1670
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|u https://doi.org/10.1007/BFb0092831
|z Full Text via HEAL-Link
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|a ZDB-2-SMA
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|a ZDB-2-LNM
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|a ZDB-2-BAE
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|a Mathematics and Statistics (Springer-11649)
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