The Resource Spectral and dynamical stability of nonlinear waves, Todd Kapitula, Keith Promislow
Spectral and dynamical stability of nonlinear waves, Todd Kapitula, Keith Promislow
Resource Information
The item Spectral and dynamical stability of nonlinear waves, Todd Kapitula, Keith Promislow represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Spectral and dynamical stability of nonlinear waves, Todd Kapitula, Keith Promislow represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
- 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
- Language
- eng
- Extent
- xiii, 361 pages
- 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
- Isbn
- 9781461469940
- Label
- Spectral and dynamical stability of nonlinear waves
- Title
- Spectral and dynamical stability of nonlinear waves
- Statement of responsibility
- Todd Kapitula, Keith Promislow
- 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
- 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
- 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
- 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
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Spectral-and-dynamical-stability-of-nonlinear/INWd5gJ3hsA/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Spectral-and-dynamical-stability-of-nonlinear/INWd5gJ3hsA/">Spectral and dynamical stability of nonlinear waves, Todd Kapitula, Keith Promislow</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>
