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...
Gardado en:
| Autor Principal: | |
|---|---|
| Formato: | Livre numérique |
| Idioma: | Anglais |
| Publicado: |
Berlin [etc.] :
Springer
[20..].
Cham : Springer Nature |
| Series: | Lecture notes in mathematics
1670 |
| Sujets: | |
| Acceso en liña: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
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 |
Table des matières:
- 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.