Sobolev Gradients and Differential Equations

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 numer...

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Κύριος συγγραφέας: neuberger, john (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1997.
Έκδοση:1st ed. 1997.
Σειρά:Lecture Notes in Mathematics, 1670
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
Περιγραφή
Περίληψη: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.
Φυσική περιγραφή:VIII, 152 p. online resource.
ISBN:9783540695943
ISSN:0075-8434 ;
DOI:10.1007/BFb0092831