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- catalog abstract "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 numerical and theoretical matters. Several concrete applications are made to illustrate the method. These applications include (1) Ginzburg-Landau functionals of superconductivity, (2) problems of transonic flow in which type depends locally on nonlinearities, and (3) minimal surface problems. Sobolev gradient constructions rely on a study of orthogonal projections onto graphs of closed densely defined linear transformations from one Hilbert space to another. These developments use work of Weyl, von Neumann and Beurling.".
- catalog contributor b10564035.
- catalog created "1997.".
- catalog date "1997".
- catalog date "1997.".
- catalog dateCopyrighted "1997.".
- catalog description "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 numerical and theoretical matters. Several concrete applications are made to illustrate the method. These applications include (1) Ginzburg-Landau functionals of superconductivity, (2) problems of transonic flow in which type depends locally on nonlinearities, and (3) minimal surface problems. Sobolev gradient constructions rely on a study of orthogonal projections onto graphs of closed densely defined linear transformations from one Hilbert space to another. These developments use work of Weyl, von Neumann and Beurling.".
- catalog description "Includes bibliographical references and index.".
- catalog extent "viii, 149 p. :".
- catalog hasFormat "Sobolev gradients and differential equations.".
- catalog identifier "3540635378".
- catalog isFormatOf "Sobolev gradients and differential equations.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1670.".
- catalog isPartOf "Lecture notes in mathematics ; 1670".
- catalog issued "1997".
- catalog issued "1997.".
- catalog language "eng".
- catalog publisher "New York : Springer-Verlag,".
- catalog relation "Sobolev gradients and differential equations.".
- catalog subject "510 s 515/.353 21".
- catalog subject "Differential equations Numerical solutions.".
- catalog subject "Differential equations, partial.".
- catalog subject "Mathematics.".
- catalog subject "Numerical analysis.".
- catalog subject "QA3 .L28 no. 1670 QA372".
- catalog subject "Sobolev gradients.".
- catalog title "Sobolev gradients and differential equations / John W. Neuberger.".
- catalog type "text".