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Spectral and dynamical stability of nonlinear waves / Todd Kapitula, Keith Promislow.
| Author/creator | Kapitula, Todd |
| Other author | Promislow, Keith, 1964- |
| Format | Electronic |
| Publication Info | New York, NY : Springer Verlag [2013] |
| Description | xiii, 361 pages : illustrations ; 24 cm. |
| Supplemental Content | Full text available from Springer Books |
| Supplemental Content | Full text available from Springer Nature - Springer Mathematics and Statistics eBooks 2013 English International |
| Subjects |
| Series | Applied mathematical sciences, 0066-5452 ; volume 185 Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 185. |
| 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. |
| 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. |
| Bibliography note | Includes bibliographical references (pages 345-357) and index. |
| Access restriction | Available only to authorized users. |
| Other forms | Also issued online. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2013934712 |
| ISBN | 9781461469940 (acid-free paper) |
| ISBN | 1461469945 (acid-free paper) |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | ✔ Available |