| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNIPARTHENOPE000011345 |
|
|
Autore |
Davis, Martin <1928- > |
|
|
Titolo |
Computability & unsolvability |
|
|
|
|
|
Pubbl/distr/stampa |
|
|
New York [etc.] : McGraw-Hill, 1958 |
|
|
|
|
|
|
|
Descrizione fisica |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Collocazione |
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
2. |
Record Nr. |
UNINA9910146292203321 |
|
|
Autore |
Neuberger J. W (John W.), <1934-> |
|
|
Titolo |
Sobolev gradients and differential equations / / J. W. Neuberger |
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Berlin, Germany ; ; New York, New York : , : Springer, , [1997] |
|
©1997 |
|
|
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
Edizione |
[1st ed. 1997.] |
|
|
|
|
|
Descrizione fisica |
|
1 online resource (VIII, 152 p.) |
|
|
|
|
|
|
Collana |
|
Lecture Notes in Mathematics, , 0075-8434 ; ; 1670 |
|
|
|
|
|
|
Classificazione |
|
|
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Differential equations - Numerical solutions |
Sobolev gradients |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Note generali |
|
Bibliographic Level Mode of Issuance: Monograph |
|
|
|
|
|
|
Nota di bibliografia |
|
Includes bibliographical references (pages [145]-149) and index. |
|
|
|
|
|
|
Nota di contenuto |
|
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. |
|
|
|
|
|
|
Sommario/riassunto |
|
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. |
|
|
|
|
|
|
|
| |