Ukrainian Mathematical Journal

, Volume 45, Issue 4, pp 564–580 | Cite as

G-convergence of periodic parabolic operators with a small parameter by the time derivative

  • N. R. Sidenko


In this paper, we consider a sequenceP k of divergent parabolic operators of the second order, which are periodic in time with periodT=const, and a sequenceP Ψ k of shifts of these operators by an arbitrary periodic vector function Ψ εX=L2((0,T) × Ω)n where Ω is a bounded Lipschitz domain in the space ℝn. The compactness of the family {P Ψ k ¦ Ψ εX, k ε ℕ ink with respect to strongG-convergence, the convergence of arbitrary solutions of the equations with the operatorP Ψ k , and the local character of the strongG-convergence in Ω are proved under the assumptions that the matrix of coefficients ofL2 is uniformly elliptic and bounded and that their time derivatives are uniformly bounded in the space L2(Ω;L2(0,T)).


Time Derivative Small Parameter Vector Function Lipschitz Domain Local Character 
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Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • N. R. Sidenko
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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