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Nonlinear Oscillations of Hamiltonian PDEs
Many partial differential equations (PDEs) that arise in physics can be viewed as infinite-dimensional Hamiltonian systems. This monograph presents recent existence results of nonlinear oscillations of Hamiltonian PDEs, particularly of periodic solutions for completely resonant nonlinear wave equati...
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| Auteur principal : | |
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| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Nonlinear Oscillations of Hamiltonian PDEs / Massimiliano Berti. |
| Édition : | 1st ed. 2007. |
| Publié : |
Boston, MA :
Birkhäuser Boston
, [20..] Cham : Springer Nature |
| Collection : | Progress in nonlinear differential equations and their applications (Online) ; 74 |
| Accès en ligne : |
Accès Nantes Université
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| Note sur l'URL : | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex |
| Condition d'utilisation et de reproduction : | Conditions particulières de réutilisation pour les bénéficiaires des licences nationales : https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |
| Contenu : | Finite Dimension. Infinite Dimension. A Tutorial in Nash Moser Theory. Application to the Nonlinear Wave Equation. Forced Vibrations. |
| Sujets : | |
| Documents associés : | Autre format:
Nonlinear oscillations of Hamiltonian PDEs |
| Résumé : | Many partial differential equations (PDEs) that arise in physics can be viewed as infinite-dimensional Hamiltonian systems. This monograph presents recent existence results of nonlinear oscillations of Hamiltonian PDEs, particularly of periodic solutions for completely resonant nonlinear wave equations. After introducing the reader to classical finite-dimensional dynamical system theory, including the Weinstein Moser and Fadell Rabinowitz resonant center theorems, the author develops the analogous theory for completely resonant nonlinear wave equations. Within this theory, both problems of small divisors and infinite bifurcation phenomena occur, requiring the use of Nash Moser theory as well as minimax variational methods. These techniques are presented in a self-contained manner together with other basic notions of Hamiltonian PDEs and number theory. This text serves as an introduction to research in this fascinating and rapidly growing field. Graduate students and researchers interested in nonlinear variational techniques as well in small divisors problems applied to Hamiltonian PDEs will find inspiration in the book. |
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| Notes : | L'impression du document génère 190 p. |
| ISBN : | 978-0-8176-4681-3 |
| DOI : | 10.1007/978-0-8176-4681-3 |