On the asymptotic expansion of Green's function for the heat conduction equation with small parameter

This work is devoted to an investigation of the asymptotic expansion for $\alpha\to0$ of Green's function $\Gamma(x,t;x_0)$ for the first boundary value problem for the equation $\Gamma_t(x,t;x_0)=\alpha^2\Gamma_{xx}(x,t;x_0)$ for the case of a moving boundary. The asymptotic expansion is obtained by means of a modification of the method of heat potentials.
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