The homogenization of diffusion-convection equations in non-periodic structures

Abstract

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). The sequence 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, with square-summable derivatives