Attractors of Hamiltonian Nonlinear Partial Differential Equations

Description

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.

Alexander Komech is Senior Scientist in the Faculty of Mathematics at the University of Vienna, the Institute for Information Transmission Problems at the Russian Academy of Sciences, and the Mechanics-Mathematics Department of Moscow State University (Lomonosov). He was awarded the Humboldt Research Award in 2006. He previously authored three monographs and the textbook Principles of Partial Differential Equations (2009). Elena Kopylova is Senior Scientist in the Faculty of Mathematics at the University of Vienna and the Institute for Information Transmission Problems at the Russian Academy of Sciences. Her research interests include the convergence to equilibrium measures for hyperbolic PDEs and global attractors of nonlinear Hamiltonian PDEs. She is the author of Dispersion Decay and Scattering Theory (2012).