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Spectral and Dynamical Stability of Nonlinear Waves

This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes fundamental ideas of the past 20+ years of research, carefully balancing theory and application. The book isolates and methodically develops key ideas by working...

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Bibliografiske detaljer
Main Authors: Kapitula, Todd. (Author, http://id.loc.gov/vocabulary/relators/aut), Promislow, Keith. (http://id.loc.gov/vocabulary/relators/aut)
Institution som forfatter: SpringerLink (Online service)
Format: Electronisk eBog
Sprog:English
Udgivet: New York, NY : Springer New York : Imprint: Springer, 2013.
Udgivelse:1st ed. 2013.
Serier:Applied Mathematical Sciences, 185
Fag:
Partial differential equations.
Statistical physics.
Dynamics.
Ergodic theory.
Partial Differential Equations.
Applications of Nonlinear Dynamics and Chaos Theory.
Dynamical Systems and Ergodic Theory.
Online adgang:https://doi.org/10.1007/978-1-4614-6995-7
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Indholdsfortegnelse:
  • Introduction
  • Background material and notation
  • Essential and absolute spectra
  • Dynamical implications of spectra: dissipative systems
  • Dynamical implications of spectra: Hamiltonian systems
  • Dynamical implications of spectra: Hamiltonian systems
  • Point spectrum: reduction to finite-rank eigenvalue problems
  • Point spectrum: linear Hamiltonian systems
  • The Evans function for boundary value problems
  • The Evans function for Sturm-Liouville operators on the real line
  • The Evans function for nth-order operators on the real line
  • Index
  • References.    .

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