A rigorous justification of the Matthews-Cox approximation for the Nikolaevskiy equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:262

Article

Zimmermann, Dominik¹ 

[1] Univ Stuttgart, IADM, Pfaffenwaldring 57, D-70569 Stuttgart, Germany

关键词: Amplitude equations;    Multiscale analysis;    Approximation;    Pattern formation;   

DOI  :  10.1016/j.jde.2017.02.005

来源: Elsevier

【 摘 要 】

The Nikolaevskiy equation is an example of a pattern forming system with marginally stable long modes. It has the unusual property that the typical Ginzburg Landau scaling ansatz for the description of propagating patterns does not yield asymptotically consistent amplitude equations. Instead, another scaling proposed by Matthews and Cox can be used to formally derive a consistent system of modulation equations. We give a rigorous proof that this system makes correct predictions about the dynamics of the Nikolaevskiy equation. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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