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The Resource Spectral and dynamical stability of nonlinear waves, Todd Kapitula, Keith Promislow

Spectral and dynamical stability of nonlinear waves, Todd Kapitula, Keith Promislow

Label
Spectral and dynamical stability of nonlinear waves
Title
Spectral and dynamical stability of nonlinear waves
Statement of responsibility
Todd Kapitula, Keith Promislow
Creator
Contributor
Author
Subject
Language
eng
Summary
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 -- Publisher's website
Member of
Additional physical form
Also issued online.
Cataloging source
BTCTA
http://library.link/vocab/creatorName
Kapitula, Todd
Dewey number
515.353
Illustrations
illustrations
Index
index present
LC call number
QA927
LC item number
.K258 2013
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1964-
http://library.link/vocab/relatedWorkOrContributorName
Promislow, Keith
Series statement
Applied mathematical sciences,
Series volume
volume 185
http://library.link/vocab/subjectName
  • Nonlinear waves
  • Nonlinear wave equations
  • Frequency stability
Label
Spectral and dynamical stability of nonlinear waves, Todd Kapitula, Keith Promislow
Instantiates
Publication
Copyright
Bibliography note
Includes bibliographical references (pages 345-357) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier.
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
Introduction -- Background materials and notation -- Essential and absolute spectra -- Asymptotic stability of waves in dissipative systems -- Orbital stability of waves in 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
Control code
828487910
Dimensions
24 cm
Extent
xiii, 361 pages
Isbn
9781461469940
Isbn Type
(acid-free paper
Lccn
2013934712
Media category
unmediated
Media MARC source
rdamedia.
Media type code
  • n
Other physical details
illustrations
System control number
(OCoLC)828487910
Label
Spectral and dynamical stability of nonlinear waves, Todd Kapitula, Keith Promislow
Publication
Copyright
Bibliography note
Includes bibliographical references (pages 345-357) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier.
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
Introduction -- Background materials and notation -- Essential and absolute spectra -- Asymptotic stability of waves in dissipative systems -- Orbital stability of waves in 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
Control code
828487910
Dimensions
24 cm
Extent
xiii, 361 pages
Isbn
9781461469940
Isbn Type
(acid-free paper
Lccn
2013934712
Media category
unmediated
Media MARC source
rdamedia.
Media type code
  • n
Other physical details
illustrations
System control number
(OCoLC)828487910

Library Locations

    • Mathematical Sciences LibraryBorrow it
      104 Ellis Library, Columbia, MO, 65201, US
      38.944377 -92.326537
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