Nonlinear Oscillations of Hamiltonian PDEs: 74 - Rilegato

Berti, Massimiliano

Rilegato

ISBN 10: 0817646809 ISBN 13: 9780817646806

Casa editrice: Springer Basel AG, 2007

Riassunto

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 bifurcation results, the author develops the analogous theory for nonlinear wave equations. The theory and applications of the Nash–Moser theorem to a class of nonlinear wave equations is also discussed together with other basic notions of Hamiltonian PDEs and number theory. The main examples of Hamiltonian PDEs presented include: the nonlinear wave equation, the nonlinear Schrödinger equation, beam equations, and the Euler equations of hydrodynamics.

This text serves as an introduction to research in this fascinating and rapidly growing field. Graduate students and researchers interested in variational techniques and nonlinear analysis applied to Hamiltonian PDEs will find inspiration in the book.

Su questo libro

Dalla quarta di copertina

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.

Dettagli dell'edizione

• Editore: Springer Basel AG
• Data di pubblicazione: 2007
• Lingua: Inglese
• ISBN 10: 0817646809
• ISBN 13: 9780817646806
• Rilegatura: Copertina rigida
• Numero di pagine: 200
• Contatto del produttore: non disponibile
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