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...
Guardat en:
| Autor principal: | |
|---|---|
| Format: | Livre numérique |
| Idioma: | Anglais |
| Publicat: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Edició: | 2nd edition. |
| Col·lecció: | Lecture Notes in Mathematics
1670 |
| Matèries: | |
| Accés en línia: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
L'impression du document génère 280 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) Version électronique de la seconde édition datant de 2010 |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Sobolev gradients and differential equations, J. W. Neuberger, 2nd edition, 2010, Berlin, Springer, 1 vol. (XIII-289 p.), Lecture notes in mathematics, 978-3-642-04040-5 |
Taula de continguts:
- 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.
- 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'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'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