Sobolev Gradients and Differential Equations (Record no. 10227)
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000 -LEADER | |
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fixed length control field | 03474nam a22004815i 4500 |
001 - CONTROL NUMBER | |
control field | 978-3-540-69594-3 |
003 - CONTROL NUMBER IDENTIFIER | |
control field | DE-He213 |
005 - DATE AND TIME OF LATEST TRANSACTION | |
control field | 20190213151316.0 |
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
fixed length control field | cr nn 008mamaa |
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
fixed length control field | 121227s1997 gw | s |||| 0|eng d |
020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
International Standard Book Number | 9783540695943 |
-- | 978-3-540-69594-3 |
024 7# - OTHER STANDARD IDENTIFIER | |
Standard number or code | 10.1007/BFb0092831 |
Source of number or code | doi |
050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
Classification number | QA370-380 |
072 #7 - SUBJECT CATEGORY CODE | |
Subject category code | PBKJ |
Source | bicssc |
072 #7 - SUBJECT CATEGORY CODE | |
Subject category code | MAT007000 |
Source | bisacsh |
072 #7 - SUBJECT CATEGORY CODE | |
Subject category code | PBKJ |
Source | thema |
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
Classification number | 515.353 |
Edition number | 23 |
100 1# - MAIN ENTRY--PERSONAL NAME | |
Personal name | Neuberger, John William. |
Relator term | author. |
Relator code | aut |
-- | http://id.loc.gov/vocabulary/relators/aut |
245 10 - TITLE STATEMENT | |
Title | Sobolev Gradients and Differential Equations |
Medium | [electronic resource] / |
Statement of responsibility, etc | by John William Neuberger. |
264 #1 - | |
-- | Berlin, Heidelberg : |
-- | Springer Berlin Heidelberg : |
-- | Imprint: Springer, |
-- | 1997. |
300 ## - PHYSICAL DESCRIPTION | |
Extent | VIII, 152 p. |
Other physical details | online resource. |
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-- | text |
-- | txt |
-- | rdacontent |
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-- | computer |
-- | c |
-- | rdamedia |
338 ## - | |
-- | online resource |
-- | cr |
-- | rdacarrier |
347 ## - | |
-- | text file |
-- | |
-- | rda |
490 1# - SERIES STATEMENT | |
Series statement | Lecture Notes in Mathematics, |
International Standard Serial Number | 0075-8434 ; |
Volume number/sequential designation | 1670 |
505 0# - FORMATTED CONTENTS NOTE | |
Formatted contents note | 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. |
520 ## - SUMMARY, ETC. | |
Summary, etc | 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. |
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical term or geographic name as entry element | Differential equations, partial. |
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical term or geographic name as entry element | Numerical analysis. |
650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical term or geographic name as entry element | Partial Differential Equations. |
-- | http://scigraph.springernature.com/things/product-market-codes/M12155 |
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical term or geographic name as entry element | Numerical Analysis. |
-- | http://scigraph.springernature.com/things/product-market-codes/M14050 |
710 2# - ADDED ENTRY--CORPORATE NAME | |
Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
773 0# - HOST ITEM ENTRY | |
Title | Springer eBooks |
776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
Display text | Printed edition: |
International Standard Book Number | 9783662182192 |
776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
Display text | Printed edition: |
International Standard Book Number | 9783540635376 |
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
Uniform title | Lecture Notes in Mathematics, |
-- | 0075-8434 ; |
Volume number/sequential designation | 1670 |
856 40 - ELECTRONIC LOCATION AND ACCESS | |
Uniform Resource Identifier | https://doi.org/10.1007/BFb0092831 |
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-- | ZDB-2-SMA |
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-- | ZDB-2-LNM |
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