000			02753nam a22002177a 4500
003			OSt
005			20240829160309.0
008			220621b |||||||| |||| 00| 0 eng d
020			_a9783642040405
040			_cDonation by Prof. A S Vasudeva Murthy _aICTS-TIFR
050			_aQA3
100			_aNeuberger, J. W.
245			_aSobolev gradients and differential equations _b- 2nd Ed.
250			_a2nd ed.
260			_aNew York: _bSpringer, _c[c1997]
300			_a289 p
490			_aLecture Notes in Mathematics _v1670
505			_a1. Several Gradients 2. Comparison of Two Gradients 3. Continuous Steepest Descent in Hilbert Space: Linear Case 4. Continuous Steepest Descent in Hilbert Space: Nonlinear Case 5. Orthogonal Projections, Adjoints and Laplacians 6. Ordinary Differential Equations and Sobolev Gradients 7. Convexity and Gradient Inequalities 8. Boundary and Supplementary Conditions 9. Continuous Newton’s Method 10. More About Finite Differences 11. Sobolev Gradients for Variational Problems 12. An Introduction to Sobolev Gradients in Non-Inner Product Spaces 13. Singularities and a Simple Ginzburg-Landau Functional 14. The Superconductivity Equations of Ginzburg-Landau 15. Tricomi Equation: A Case Study 16. Minimal Surfaces 17. Flow Problems and Non-Inner Product Sobolev Spaces 18. An Alternate Approach to Time-dependent PDEs 19. Foliations and Supplementary Conditions I 20. Foliations and Supplementary Conditions II 21. Some Related Iterative Methods for Differential Equations 22. An Analytic Iteration Method 23. Steepest Descent for Conservation Equations 24. Code for an Ordinary Differential Equation 25. Geometric Curve Modeling with Sobolev Gradients 26. Numerical Differentiation, Sobolev Gradients 27. Steepest Descent and Newton’s Method and Elliptic PDE 28. Ginzburg-Landau Separation Problems 29. Numerical Preconditioning Methods for Elliptic PDEs 30. More Results on Sobolev Gradient Problems 31. Notes and Suggestions for Future Work
520			_aA 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 versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside from the first edition of this work, this is the only known account of Sobolev gradients in book form.
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999			_c3161 _d3161