Abstract
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 kΨ 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 kΨ ¦ Ψ εX, k ε ℕ ink with respect to strongG-convergence, the convergence of arbitrary solutions of the equations with the operatorP kΨ , and the local character of the strongG-convergence in Ω are proved under the assumptions that the matrix of coefficients ofL 2 is uniformly elliptic and bounded and that their time derivatives are uniformly bounded in the space L2(Ω;L2(0,T)).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 4, pp. 525–538, April, 1993.
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Sidenko, N.R. G-convergence of periodic parabolic operators with a small parameter by the time derivative. Ukr Math J 45, 564–580 (1993). https://doi.org/10.1007/BF01062952
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DOI: https://doi.org/10.1007/BF01062952