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...
Κύριος συγγραφέας: | |
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Συγγραφή απο Οργανισμό/Αρχή: | |
Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
Γλώσσα: | English |
Έκδοση: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
1997.
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Έκδοση: | 1st ed. 1997. |
Σειρά: | Lecture Notes in Mathematics,
1670 |
Θέματα: | |
Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- 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.