Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry]
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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2005, Volume 1, Number 1, Pages 3–34 (Mi jmag1)  
This article is cited in 6 scientific papers (total in 6 papers)

Travelling waves dynamics in a nonlinear parabolic equation with a shifted spatial argument

E. P. Belan

Department of Mathematics and Information Science V.I. Vernadsky Tavrida National University 4 Vernadsky Str., Simpheropol, 95036, Ukraine
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Abstract: The local dynamics of a nonlinear parabolic equation on a circle with a shifted spatial argument and a small diffusion is studied. It is proved that the travelling waves interaction satisfies to 1:2 principle. The maximum principle for amplitudes with coefficient 2/3 is established. A number of stable travelling waves increases when the diffusion coeffcient tends to zero.
Key words and phrases: parabolic equations, running waves, stability.
Received: 29.06.2004
Bibliographic databases:
Document Type: Article
MSC: 35Q60, 35R10, 37L10
Language: Russian
Citation: E. P. Belan, “Travelling waves dynamics in a nonlinear parabolic equation with a shifted spatial argument”, Zh. Mat. Fiz. Anal. Geom., 1:1 (2005), 3–34
Citation in format AMSBIB
\Bibitem{Bel05}
\by E.~P.~Belan
\paper Travelling waves dynamics in a nonlinear parabolic equation with a shifted spatial argument
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2005
\vol 1
\issue 1
\pages 3--34
\mathnet{http://mi.mathnet.ru/jmag1}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2170082}
\zmath{https://zbmath.org/?q=an:1098.35075}
\elib{https://elibrary.ru/item.asp?id=13421669}
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    • This publication is cited in the following 6 articles:
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