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

Анотація

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 coeffient tends to zero.

Mathematics Subject Classification: 35Q60, 35R10, 37L10.

Ключові слова:

parabolic equations, running waves, stability

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Як цитувати

(1)
E. P. Belan, Travelling waves dynamics in a nonlinear parabolic equation with a shifted spatial argument, Журн. мат. фіз. анал. геом. 1 (2005), 3-34.

Номер

Том 1 № 1 (2005)

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