Sobolev gradients and differential equations
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 numer...
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| Autor principal: | |
|---|---|
| Formato: | Livre numérique |
| Lenguaje: | Anglais |
| Publicado: |
Berlin [etc.] :
Springer
[20..].
Cham : Springer Nature |
| Colección: | Lecture notes in mathematics
1670 |
| Materias: | |
| Acceso en línea: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
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Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Sobolev gradients and differential equations, J. W. Neuberger, 1997, Berlin, Springer, 1 vol. (VIII-149 p.), Lecture notes in mathematics, 3-540-63537-8 • Sobolev Gradients and Differential Equations, Texte imprimé, 9783662182192 |
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| 100 | 1 | |a Neuberger, John W., |d 1934-2020, |c mathématicien. | |
| 245 | 1 | 0 | |a Sobolev gradients and differential equations |c J. W. Neuberger. |
| 260 | |a Berlin [etc.] : |b Springer. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Lecture notes in mathematics |v 1670 |x 1617-9692 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 0 | |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. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |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. | ||
| 650 | |a Équations aux dérivées partielles | ||
| 650 | |a Sobolev, Espaces de | ||
| 650 | |a Analyse numérique | ||
| 650 | |a Équations différentielles |x Solutions numériques | ||
| 650 | |a Mathématiques | ||
| 650 | |a Gradients de Sobolev | ||
| 776 | 0 | |0 032513941 |t Sobolev gradients and differential equations |f J. W. Neuberger |d 1997 |c Berlin |n Springer |p 1 vol. (VIII-149 p.) |s Lecture notes in mathematics |z 3-540-63537-8 | |
| 776 | 0 | |t Sobolev Gradients and Differential Equations |b Texte imprimé |z 9783662182192 | |
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| 856 | 4 | |5 452349901:750660120 |u https://ezproxy.univ-orleans.fr/login?url=https://doi.org/10.1007/BFb0092831 |z Accès Université d'Orléans | |
| 856 | 4 | |5 180339901:754009742 |u https://ezproxy.insa-cvl.fr/login?qurl=https://doi.org/10.1007/BFb0092831 |z Accès INSA CVL | |
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