On the decay rate of solutions of linear parabolic equations for infinitely increasing time

The first boundary value problem with zero boundary values is considered for a one-dimensional linear parabolic equation. If the equation is sufficiently close to the heat equation, the rate of decreasing for the solution is connected with the number of zero level lines of the solution, nonvanishing for all values of time. Bibliography: 4 titles. Translated from Trudy Seminara imeni I.G. Petrovskogo, No. 17, pp. 118–127, 1994.