Asymptotics of the Solution to the Cauchy Problem for Linear Parabolic Equations of Second Order with Small Diffusion

This paper is devoted to constructing an asymptotics of the solution to the Cauchy problem for a linear parabolic equation of second order with variable coefficients containing a small parameter at the highest derivative. Sufficient conditions for the existence and uniqueness of the “multiplicative” asymptotic expansion of the global solution of the problem are given.