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

  • N. R. Sidenko

Abstract

In this paper, we consider a sequence Pk of divergent parabolic operators of the second order, which are periodic in time with period T=const, and a sequence Pkψ of shifts of these operators by an arbitrary periodic vector function ψX={L2((0,T)×Ω)}n where Ω is a bounded Lipschitz domain in the space Rn. The compactness of the family {PΨk¦ΨX,k} in k with respect to strong G-convergence, the convergence of arbitrary solutions of the equations with the operator Pkψ, and the local character of the strong G-convergence in Ω are proved under the assumptions that the matrix of coefficients of L2 is uniformly elliptic and bounded and that their time derivatives are uniformly bounded in the space L2(Ω;L2(0,T)).
Published
25.04.1993
How to Cite
Sidenko, N. R. “G-Convergence of Periodic Parabolic Operators With a Small Parameter by the Time Derivative”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 45, no. 4, Apr. 1993, pp. 525–538, https://umj.imath.kiev.ua/index.php/umj/article/view/5840.
Section
Research articles