Theorems related to the asymptotic proximity of fundamental solutions to parabolic equations (Q1363284)

In an interesting work by \textit{V. V. Zhikov} [Differ. Equations 25, 33-39, translation from Differ. Uravn. 25, 44-50 (1989; Zbl 0695.35014)], a theorem concerning the proximity of fundamental solutions (FS) to the Cauchy problem for equations with periodic coefficients is proved. Here we establish a different approach in order to obtain theorems concerning the proximity of FS and other results. As usual, from the information about the proximity of FS to two equations, there follow the theorems concerning the proximity of solutions to the Cauchy problem that are constructed according to the compatible initial data.