We consider the homogenization of diffusion-convective problems with given divergence-free velocities in nonperiodic structures defined by sequences of characteristic functions(the first sequence). These quence of concentration (the second sequence)is uniformly bounded in the space of square-summable functions with square-summable derivatives with respect to spatial variables. At the same time, the sequence of time-derivative of product of these concentrations on the characteristic functions, that define a nonperiodic structure, is bounded in the space of square-summable functions from time interval into the conjugated space of functions depending on spatial variables, withsquare-summable derivatives. We prove the strong compactness of the second sequences in the space of quadratically summable functions and use this result to homogenize the corresponding boundary value problems that depend on a small parameter.
MEIRMANOV, ANVARBEK and GALTSEV, OLEG
"The homogenization of diffusion-convection equations in non-periodic structures,"
Turkish Journal of Mathematics: Vol. 44:
3, Article 31.
Available at: https://journals.tubitak.gov.tr/math/vol44/iss3/31