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Periodic modes of the phenomenological spin combustion equation

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Abstract

We consider a scalar equation in the class of semilinear parabolic equations on a circle of radius r. The problem studied here is a model of gas-free combustion on a cylindrical surface of radius r. For each r > 0, the periodic problem has a spatially inhomogeneous limit cycle, which is asymptotically orbitally stable for r < r 1. We show that, as r grows and passes through r 1, an asymptotically orbitally stable 2-torus of spatially inhomogeneous periodic solutions bifurcates from the limit cycle. The dynamics of the 2-torus of self-similar periodic solutions is studied to the range (0, l) of the parameter r − r 1, where l ∼ 1.

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Authors and Affiliations

  1. Institute for Mathematics, National Academy of Sciences, Kiev, Ukraine

    A. M. Samoilenko & E. P. Belan

  2. Tavriya National University, Simferopol’, Crimea

    A. M. Samoilenko & E. P. Belan

Authors
  1. A. M. Samoilenko
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  2. E. P. Belan
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Correspondence to A. M. Samoilenko.

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Original Russian Text © A.M. Samoilenko, E.P. Belan, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 2, pp. 211–228.

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Samoilenko, A.M., Belan, E.P. Periodic modes of the phenomenological spin combustion equation. Diff Equat 51, 214–231 (2015). https://doi.org/10.1134/S001226611502007X

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