Attractors of Hamiltonian Nonlinear Partial Differential Equations

The first monograph on the theory of global attractors of Hamiltonian partial differential equations.

Alexander Komech (Author), Elena Kopylova (Author)

9781316516911, Cambridge University Press

Hardback, published 30 September 2021

200 pages
23.5 x 15.8 x 2 cm, 0.5 kg

'It will be a very useful reference for graduate students and mathematicians working in partial differential equations and mathematical physics.' Denise Huet, zbMATH

This monograph is the first to present the theory of global attractors of Hamiltonian partial differential equations. A particular focus is placed on the results obtained in the last three decades, with chapters on the global attraction to stationary states, to solitons, and to stationary orbits. The text includes many physically relevant examples and will be of interest to graduate students and researchers in both mathematics and physics. The proofs involve novel applications of methods of harmonic analysis, including Tauberian theorems, Titchmarsh's convolution theorem, and the theory of quasimeasures. As well as the underlying theory, the authors discuss the results of numerical simulations and formulate open problems to prompt further research.

Introduction
1. Global attraction to stationary states
2. Global attraction to solitons
3. Global attraction to stationary orbits
4. Asymptotic stability of stationary orbits and solitons
5. Adiabatic effective dynamics of solitons
6. Numerical simulation of solitons
7. Dispersive decay
8. Attractors and quantum mechanics
References
Index.

Subject Areas: Mathematical physics [PHU], Quantum physics [quantum mechanics & quantum field theory PHQ], Differential calculus & equations [PBKJ]