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...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
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
Πίνακας περιεχομένων:
  • Several gradients
  • Comparison of two gradients
  • Continuous steepest descent in Hilbert space: Linear case
  • Continuous steepest descent in Hilbert space: Nonlinear case
  • Orthogonal projections, Adjoints and Laplacians
  • Introducing boundary conditions
  • Newton's method in the context of Sobolev gradients
  • Finite difference setting: the inner product case
  • Sobolev gradients for weak solutions: Function space case
  • Sobolev gradients in non-inner product spaces: Introduction
  • The superconductivity equations of Ginzburg-Landau
  • Minimal surfaces
  • Flow problems and non-inner product Sobolev spaces
  • Foliations as a guide to boundary conditions
  • Some related iterative methods for differential equations
  • A related analytic iteration method
  • Steepest descent for conservation equations
  • A sample computer code with notes.