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005 - DATE AND TIME OF LATEST TRANSACTION |
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20140310151449.0 |
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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130606s2013 xxu| s |||| 0|eng d |
020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
International Standard Book Number |
9781461469957 |
|
978-1-4614-6995-7 |
050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
Classification number |
QA370-380 |
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
Classification number |
515.353 |
Edition number |
23 |
264 #1 - |
-- |
New York, NY : |
-- |
Springer New York : |
-- |
Imprint: Springer, |
-- |
2013. |
912 ## - |
-- |
ZDB-2-SMA |
100 1# - MAIN ENTRY--PERSONAL NAME |
Personal name |
Kapitula, Todd. |
Relator term |
author. |
245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE |
Title |
Spectral and Dynamical Stability of Nonlinear Waves |
Medium |
[electronic resource] / |
Statement of responsibility, etc |
by Todd Kapitula, Keith Promislow. |
300 ## - PHYSICAL DESCRIPTION |
Extent |
XIII, 361 p. 50 illus. |
Other physical details |
online resource. |
440 1# - SERIES STATEMENT/ADDED ENTRY--TITLE |
Title |
Applied Mathematical Sciences, |
International Standard Serial Number |
0066-5452 ; |
Volume number/sequential designation |
185 |
505 0# - FORMATTED CONTENTS NOTE |
Formatted contents note |
Introduction -- Background material and notation -- Essential and absolute spectra -- Dynamical implications of spectra: dissipative systems -- Dynamical implications of spectra: Hamiltonian systems -- Dynamical implications of spectra: Hamiltonian systems -- Point spectrum: reduction to finite-rank eigenvalue problems -- Point spectrum: linear Hamiltonian systems -- The Evans function for boundary value problems -- The Evans function for Sturm-Liouville operators on the real line -- The Evans function for nth-order operators on the real line -- Index -- References. |
520 ## - SUMMARY, ETC. |
Summary, etc |
This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes fundamental ideas of the past 20+ years of research, carefully balancing theory and application. The book isolates and methodically develops key ideas by working through illustrative examples that are subsequently synthesized into general principles. Many of the seminal examples of stability theory, including orbital stability of the KdV solitary wave, and asymptotic stability of viscous shocks for scalar conservation laws, are treated in a textbook fashion for the first time. It presents spectral theory from a dynamical systems and functional analytic point of view, including essential and absolute spectra, and develops general nonlinear stability results for dissipative and Hamiltonian systems. The structure of the linear eigenvalue problem for Hamiltonian systems is carefully developed, including the Krein signature and related stability indices. The Evans function for the detection of point spectra is carefully developed through a series of frameworks of increasing complexity. Applications of the Evans function to the Orientation index, edge bifurcations, and large domain limits are developed through illustrative examples. The book is intended for first or second year graduate students in mathematics, or those with equivalent mathematical maturity. It is highly illustrated and there are many exercises scattered throughout the text that highlight and emphasize the key concepts. Upon completion of the book, the reader will be in an excellent position to understand and contribute to current research in nonlinear stability. |
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
Topical term or geographic name as entry element |
Mathematics. |
|
Topical term or geographic name as entry element |
Differentiable dynamical systems. |
|
Topical term or geographic name as entry element |
Differential equations, partial. |
|
Topical term or geographic name as entry element |
Mathematics. |
|
Topical term or geographic name as entry element |
Partial Differential Equations. |
|
Topical term or geographic name as entry element |
Nonlinear Dynamics. |
|
Topical term or geographic name as entry element |
Dynamical Systems and Ergodic Theory. |
700 1# - ADDED ENTRY--PERSONAL NAME |
Personal name |
Promislow, Keith. |
Relator term |
author. |
710 2# - ADDED ENTRY--CORPORATE NAME |
Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
773 0# - HOST ITEM ENTRY |
Title |
Springer eBooks |
776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
Display text |
Printed edition: |
International Standard Book Number |
9781461469940 |
856 40 - ELECTRONIC LOCATION AND ACCESS |
Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-1-4614-6995-7 |
942 ## - ADDED ENTRY ELEMENTS (KOHA) |
Source of classification or shelving scheme |
|
Item type |
E-Book |