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Integral manifolds and exponential splitting of linear parabolic equations with rapidly varying coefficients

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Abstract

We study linear parabolic equations with rapidly varying coefficients. It is assumed that the averaged equation corresponding to the source equation admits exponential splitting. We establish conditions under which the source equation also admits exponential splitting. It is shown that integral manifolds play an important role in constructing transformations that split the equations under consideration. To prove the existence of integral manifolds, we apply Zhikov's results on the justification of the averaging method for linear parabolic equations.

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Authors and Affiliations

  1. Simferopol University, Simferopol

    E. P. Belan

  2. Institute of Mathematics Ukrainian, Academy of Sciences, Kiev

    O. B. Lykova

Authors
  1. E. P. Belan
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  2. O. B. Lykova
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 12, pp. 1593–1608, December, 1995.

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Belan, E.P., Lykova, O.B. Integral manifolds and exponential splitting of linear parabolic equations with rapidly varying coefficients. Ukr Math J 47, 1818–1836 (1995). https://doi.org/10.1007/BF01060957

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  • DOI: https://doi.org/10.1007/BF01060957

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