An estimate for the remainder term of the asymptotics of the fundamental solution to parabolic equations with a small parameter

Abstract.

In this paper we deal with an asymptotics of the fundamental solution to parabolic equations of second order with a small parameter. We obtain a uniform multiplicative estimate of the difference between the fundamental solution and its asymptotics. We point out the asymptotics of the logarithmic limit in a special case when the matrix defining the principle term of the parabolic equation depends on the spatial variables and time.