Estimates of locally periodic and reiterated homogenization for parabolic equations

A study was conducted to investigate estimates of locally periodic and reiterated homogenization for paraboloc equations. The Cauchy problem was investigated in the half space for a parabolic equation with strongly inhomogeneous coefficients. Zhikov's method was used to introduce an additional integration parameter that made it possible to derive estimates in the case of a minimally regular solution due to a shift. The shift was found to be effective with respect to the slow variable for the problem in the first equation. An alternative spectral approach to the proof of operator estimates in homogenization was developed to solve the problem. The first approximation method was found to be more universal in the sense that it was the only one suitable for proving operator estimates in many problems.