Asymptotic analysis of the parametric instability of nonlinear hyperbolic equations

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Abstract

This paper is concerned with parametric resonance under nonlinear periodic perturbations of differential equations which are abstract analogues of hyperbolic systems. A modification of the Krylov-Bogolyubov averaging method capable of circumventing the well-known small divisor problem is applied to reduce the description of solutions of perturbed equations at resonance to the study of autonomous dynamical systems in finite-dimensional spaces.

Original languageEnglish
Pages (from-to)1088-1112
Number of pages25
JournalSbornik Mathematics
Volume208
Issue number8
DOIs
Publication statusPublished - 1 Jan 2017

Keywords

  • Averaging method
  • Hyperbolic equations
  • Parametric resonance

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