On the evolution operators for some equations of mathematical physics with variable coefficients

It is shown that, with the help of a relatively simple operator technique, it is possible to solve, from a common point of view, the Cauchy problem for many important equations of mathematical physics with variable coefficients. This result is applied to the equations of kinetic theory, and diffusion and heat conduction equations. We discuss the problem of equivalence of different schemes of expansion according to the Hausdorff formula.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 7, pp. 857–869, July, 1994.