Spectral and Dynamical Stability of Nonlinear Waves
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...
Guardat en:
| Autors principals: | , |
|---|---|
| Format: | Livre numérique |
| Idioma: | Anglais |
| Publicat: |
New York, NY :
Springer New York : Imprint: Springer
[20..].
Cham : Springer Nature |
| Edició: | 1st ed. 2013. |
| Col·lecció: | Applied Mathematical Sciences
185 |
| Accés en línia: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Spectral and dynamical stability of nonlinear waves, Todd Kapitula, Keith Promislow, New York, Springer, 2013, 1 vol. (XIII-361 p.), Applied mathematical sciences, 978-1-461-46994-0 |
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| 100 | 1 | |a Kapitula, Todd. | |
| 245 | 1 | 0 | |a Spectral and Dynamical Stability of Nonlinear Waves |c by Todd Kapitula, Keith Promislow. |
| 250 | |a 1st ed. 2013. | ||
| 260 | |a New York, NY : |b Springer New York : |b Imprint: Springer. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Applied Mathematical Sciences |v 185 |x 2196-968X | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 1 | |a 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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 | ||
| 700 | 1 | |a Promislow, Keith. |4 aut | |
| 776 | 0 | |0 171109961 |t Spectral and dynamical stability of nonlinear waves |f Todd Kapitula, Keith Promislow |c New York |n Springer |d 2013 |p 1 vol. (XIII-361 p.) |s Applied mathematical sciences |z 978-1-461-46994-0 | |
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