Differential and Integral Equations

On the stability of periodic solutions of multi-dimensional models

Rita Cavazzoni

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Abstract

We consider a class of multi-dimensional models and prove the existence of non-trivial steady periodic waves. One of the main results is concerned with the spectral instability of a stationary periodic wave, proved by means of Floquet's theory and the introduction of the Evans function for a suitable related eigenvalue problem. A description of the zero set of the Evans function around the origin allows us to establish a link between the spectral stability analysis and a first-order system of conservation laws derived from the original model through homogenisation.

Article information

Source
Differential Integral Equations, Volume 20, Number 2 (2007), 181-196.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039512

Mathematical Reviews number (MathSciNet)
MR2294464

Zentralblatt MATH identifier
1212.35061

Subjects
Primary: 35L65: Conservation laws
Secondary: 35B10: Periodic solutions 35B35: Stability 35G25: Initial value problems for nonlinear higher-order equations 35K55: Nonlinear parabolic equations

Citation

Cavazzoni, Rita. On the stability of periodic solutions of multi-dimensional models. Differential Integral Equations 20 (2007), no. 2, 181--196. https://projecteuclid.org/euclid.die/1356039512


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