Sobolev gradients and differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1997
|
| Series: | Lecture notes in mathematics
1670 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 149 S. Ill. |
| ISBN: | 3540635378 |
Staff View
MARC
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| 100 | 1 | |a Neuberger, John W. |d 1934- |e Verfasser |0 (DE-588)115580158 |4 aut | |
| 245 | 1 | 0 | |a Sobolev gradients and differential equations |c J. W. Neuberger |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1997 | |
| 300 | |a VIII, 149 S. |b Ill. | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1670 | |
| 650 | 4 | |a Partielle Differentialgleichung - Gradientenverfahren | |
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| 650 | 4 | |a Sobolev gradients | |
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Record in the Search Index
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| adam_text | Contents
Preface v
Chapter 1. Several Gradients 1
Chapter 2. Comparison of Two Gradients 5
Chapter 3. Continuous Steepest Descent in Hilbert Space: Linear Case 11
Chapter 4. Continuous Steepest Descent in Hilbert Space: Nonlinear Case 15
1. Global Existence 15
2. Gradient Inequality 16
3. Convexity 23
4. Examples 27
5. Higher Order Sobolev Spaces for Lower Order Problems 29
Chapter 5. Orthogonal Projections, Adjoints and Laplacians 33
1. A Construction of a Sobolev Space. 33
2. A Formula of Von Neumann 35
3. Relationship between Adjoints 36
4. General Laplacians 37
5. A Generalized Lax Milgram Theorem 38
6. Laplacians and Closed Linear Transformations 39
7. Remarks on Higher Order Sobolev Spaces 42
Chapter 6. Introducing Boundary Conditions 43
1. Projected Gradients 43
2. Approximation of Projected Gradients 48
3. Singular Boundary Value Problems 49
4. Dual Steepest Descent 50
5. Multiple Solutions of Some Elliptic Problems 51
Chapter 7. Newton s Method in the Context of Sobolev Gradients 53
1. Newton Directions From an Optimization. 53
2. Generalized Inverses and Newton s Method. 55
Chapter 8. Finite Difference Setting: the Inner Product Case 59
Chapter 9. Sobolev Gradients for Weak Solutions: Function Space Case 69
VIII CONTENTS
Chapter 10. Sobolev Gradients in Non inner Product Spaces: Introduction 75
Chapter 11. The Superconductivity Equations of Ginzburg Landau 79
1. Introduction 79
2. The GL F inctional 79
3. A Simple Example of a Sobolev Gradient 80
4. A Sobolev Gradient for GL. 81
5. Finite Dimensional Emulation 83
6. Numerical Results 84
7. A Liquid Crystal Problem 85
8. An Elasticity Problem 85
9. Singularities for a Simpler GL functional 86
10. Some Plots 88
Chapter 12. Minimal Surfaces 93
1. Introduction 93
2. Minimum Curve Length 93
3. Minimal Surfaces 95
4. Uniformly Parameterized Surfaces 99
5. Numerical Methods and Test Results 102
6. Conclusion 106
Chapter 13. Flow Problems and Non inner Product Sobolev Spaces 107
1. Full Potential Equation 107
2. A Linear Mixed Type Problem 110
3. Other Codes for Transonic Flow 110
4. Transonic Flow Plots 112
Chapter 14. Foliations as a Guide to Boundary Conditions 115
1. A Foliation Theorem 115
2. Another Solution Giving Nonlinear Projection 123
Chapter 15. Some Related Iterative Methods for Differential Equations 125
Chapter 16. A Related Analytic Iteration Method 135
Chapter 17. Steepest Descent for Conservation Equations 139
Chapter 18. A Sample Computer Code with Notes 141
Bibliography 145
Index 150
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:12:54Z |
| institution | BVB |
| isbn | 3540635378 |
| language | English |
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| physical | VIII, 149 S. Ill. |
| publishDate | 1997 |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Neuberger, John W. 1934- Verfasser (DE-588)115580158 aut Sobolev gradients and differential equations J. W. Neuberger Berlin [u.a.] Springer 1997 VIII, 149 S. Ill. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1670 Partielle Differentialgleichung - Gradientenverfahren Differential equations Numerical solutions Sobolev gradients Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Gradientenverfahren (DE-588)4157995-1 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Gradientenverfahren (DE-588)4157995-1 s DE-604 Lecture notes in mathematics 1670 (DE-604)BV000676446 1670 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007830224&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Neuberger, John W. 1934- Sobolev gradients and differential equations Lecture notes in mathematics Partielle Differentialgleichung - Gradientenverfahren Differential equations Numerical solutions Sobolev gradients Partielle Differentialgleichung (DE-588)4044779-0 gnd Gradientenverfahren (DE-588)4157995-1 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4157995-1 |
| title | Sobolev gradients and differential equations |
| title_auth | Sobolev gradients and differential equations |
| title_exact_search | Sobolev gradients and differential equations |
| title_full | Sobolev gradients and differential equations J. W. Neuberger |
| title_fullStr | Sobolev gradients and differential equations J. W. Neuberger |
| title_full_unstemmed | Sobolev gradients and differential equations J. W. Neuberger |
| title_short | Sobolev gradients and differential equations |
| title_sort | sobolev gradients and differential equations |
| topic | Partielle Differentialgleichung - Gradientenverfahren Differential equations Numerical solutions Sobolev gradients Partielle Differentialgleichung (DE-588)4044779-0 gnd Gradientenverfahren (DE-588)4157995-1 gnd |
| topic_facet | Partielle Differentialgleichung - Gradientenverfahren Differential equations Numerical solutions Sobolev gradients Partielle Differentialgleichung Gradientenverfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007830224&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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