| 000 | 03474nam a22004815i 4500 | ||
|---|---|---|---|
| 001 | 978-3-540-69594-3 | ||
| 003 | DE-He213 | ||
| 005 | 20190213151316.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 121227s1997 gw | s |||| 0|eng d | ||
| 020 |
_a9783540695943 _9978-3-540-69594-3 |
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| 024 | 7 |
_a10.1007/BFb0092831 _2doi |
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| 050 | 4 | _aQA370-380 | |
| 072 | 7 |
_aPBKJ _2bicssc |
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| 072 | 7 |
_aMAT007000 _2bisacsh |
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| 072 | 7 |
_aPBKJ _2thema |
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| 082 | 0 | 4 |
_a515.353 _223 |
| 100 | 1 |
_aNeuberger, John William. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
| 245 | 1 | 0 |
_aSobolev Gradients and Differential Equations _h[electronic resource] / _cby John William Neuberger. |
| 264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c1997. |
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| 300 |
_aVIII, 152 p. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
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| 490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1670 |
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| 505 | 0 | _aSeveral 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. | |
| 520 | _aA 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. | ||
| 650 | 0 | _aDifferential equations, partial. | |
| 650 | 0 | _aNumerical analysis. | |
| 650 | 1 | 4 |
_aPartial Differential Equations. _0http://scigraph.springernature.com/things/product-market-codes/M12155 |
| 650 | 2 | 4 |
_aNumerical Analysis. _0http://scigraph.springernature.com/things/product-market-codes/M14050 |
| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer eBooks | |
| 776 | 0 | 8 |
_iPrinted edition: _z9783662182192 |
| 776 | 0 | 8 |
_iPrinted edition: _z9783540635376 |
| 830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1670 |
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| 856 | 4 | 0 | _uhttps://doi.org/10.1007/BFb0092831 |
| 912 | _aZDB-2-SMA | ||
| 912 | _aZDB-2-LNM | ||
| 912 | _aZDB-2-BAE | ||
| 999 |
_c10227 _d10227 |
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