On Estimates of Solutions of the Split Problems for Some Multi-Dimensional Partial Differential Equations

We consider multidimensional second order parabolic equations and the first order partial differential equations. We consider various splittings of the Cauchy problem in the case when the coefficients of the equation depending on time and all space variables and have a special form. The uniform correctness of the split problems, that is, a sufficient condition for the split problems solutions convergence to the solutions to the original problems and the uniform correctness of this problem is proved in classes of smooth functions.