Attractors of Hamiltonian Nonlinear Partial Differential Equations

Inbunden, Engelska, 2021

Del 224 i serien Cambridge Tracts in Mathematics

1 331 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2021-09-30
Mått:158 x 235 x 20 mm
Vikt:500 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Tracts in Mathematics
Antal sidor:230
Förlag:Cambridge University Press
ISBN:9781316516911

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Mer om författaren

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).

Recensioner i media

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

Innehållsförteckning

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.