Nonlinear Oscillations of Hamiltonian PDEs by Massimiliano Berti

Nonlinear Oscillations of Hamiltonian PDEs by Massimiliano Berti

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.

From the reviews:

"After discussing important problems and introducing general techniques for Hamiltonian PDEs, the book under review focuses on the nonlinear wave equationThe point of view the author takes is a dynamical system perspective, giving the maximal priority to the search for invariant objects. … Some nice remarks and useful tools … are collected in the appendices. This monograph is written with high rigor and good taste and it may conveniently win the attention of both advanced researchers and graduate students." (Enrico Valdinoci, Mathematical Reviews, Issue 2008 i)

SKU	Nicht verfügbar
ISBN 13	9780817646806
ISBN 10	0817646809
Titel	Nonlinear Oscillations of Hamiltonian PDEs
Autor	Massimiliano Berti
Serie	Progress In Nonlinear Differential Equations And Their Applications
Buchzustand	Nicht verfügbar
Verlag	Birkhauser Boston Inc
Erscheinungsjahr	2007-10-01
Seitenanzahl	180
Hinweis auf dem Einband	Die Abbildung des Buches dient nur Illustrationszwecken, die tatsächliche Bindung, das Cover und die Auflage können sich davon unterscheiden.
Hinweis	Nicht verfügbar