Sobolev Gradients and Differential Equations
A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an 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. For discrete ve...
| Κύριος συγγραφέας: | |
|---|---|
| Συγγραφή απο Οργανισμό/Αρχή: | |
| Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
| Γλώσσα: | English |
| Έκδοση: |
Berlin, Heidelberg :
Springer Berlin Heidelberg,
2010.
|
| 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
- Ordinary Differential Equations and Sobolev Gradients
- Convexity and Gradient Inequalities
- Boundary and Supplementary Conditions
- Continuous Newton#x2019;s Method
- More About Finite Differences
- Sobolev Gradients for Variational Problems
- An Introduction to Sobolev Gradients in Non-Inner Product Spaces
- Singularities and a Simple Ginzburg-Landau Functional
- The Superconductivity Equations of Ginzburg-Landau
- Tricomi Equation: A Case Study
- Minimal Surfaces
- Flow Problems and Non-Inner Product Sobolev Spaces
- An Alternate Approach to Time-dependent PDEs
- Foliations and Supplementary Conditions I
- Foliations and Supplementary Conditions II
- Some Related Iterative Methods for Differential Equations
- An Analytic Iteration Method
- Steepest Descent for Conservation Equations
- Code for an Ordinary Differential Equation
- Geometric Curve Modeling with Sobolev Gradients
- Numerical Differentiation, Sobolev Gradients
- Steepest Descent and Newton#x2019;s Method and Elliptic PDE
- Ginzburg-Landau Separation Problems
- Numerical Preconditioning Methods for Elliptic PDEs
- More Results on Sobolev Gradient Problems
- Notes and Suggestions for Future Work.
