Invariant manifolds and dispersive Hamiltonian evolution equations
By: Kenji Nakanishi, Wilhelm Schlag
Contributors: Schlag, Wilhelm, 1969-
Series: Zurich lectures in advanced mathematics
Publisher: European Mathematical Society
Published: 2011
Place of publication: Zürich, Switzerland
Language: eng
Number of pages: 253
ISBN-13: 9783037190951
Subjects: Klein-Gordon equation; Invariant manifolds; Hamiltonian systems; Hyperbolic spaces
Description: "The notion of an invariant manifold arises naturally in the asymptotic stability analysis of stationary or standing wave solutions of unstable dispersive Hamiltonian evolution equations such as the focusing semilinear Klein Gordon and Schrodinger equations. [...] These lectures are suitable for graduate students and researchers in partial differential equations and mathematical physics. For the cubic Klein Gordon equation in three dimensions all details are provided, including the derivation of Strichartz estimates for the free equation and the concentration-compactness argument leading to scattering due to Kenig and Merle."--P.[4] of cover.
Notes: Includes bibliographical references (p. [241]-245) and index.
Table of contents: title: 1. Introduction; title: 2. The Klein-Gordon equation below the ground state energy; title: 3. Above the ground state energy I: near Q; title: 4. Above the ground state energy II: Moving away from Q; title: 5. Above the ground state energy III: global NLKG dynamics; title: 6. Further developments of the theory.