This paper provesthat the solution of the initial value problem for homogeneous heat conduction equation is an analytical function by the solution formula of the initial value problem for the heat conduction equation.The paper provides the gradient estimation of solutions for homogeneous heat conduction equation, offers the method of proving that the solution of homogeneous heat conduction equation is an analytical function by estimating the partial derivative of each order and applying Taylor formula.

%U https://zkxb.jsu.edu.cn/EN/10.13438/j.cnki.jdzk.2020.04.002