Sobolev Gradients and Differential Equations

Sobolev Gradients and Differential Equations (Paperback)

By J W Neuberger , John W Neuberger 
Publisher: Springer
Edition: Paperback
Language: English
ISBN: 3540635378
EAN: 9783540635376
No. of Units: 1
No. of Pages: 150
Publish Date: 2008-6-1
Binding: Paperback
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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.
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Specification

Title: Sobolev Gradients and Differential Equations
Publisher: Springer
Author: J W Neuberger , John W Neuberger
Edition: Paperback
Language: English
ISBN: 3540635378
EAN: 9783540635376
No. of Units: 1
No. of Pages: 150
Publish Date: 2008-6-1
Binding: Paperback

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