Geodesic
On the asymptotic expansion of Green's function for the heat conduction equation with small parameter
Sbornik. Mathematics, Tome 16 (1972) no. 2, pp. 209-221 
G. A. Nesenenko. On the asymptotic expansion of Green's function for the heat conduction equation with small parameter. Sbornik. Mathematics, Tome 16 (1972) no. 2, pp. 209-221. http://geodesic.mathdoc.fr/item/SM_1972_16_2_a4/
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     author = {G. A. Nesenenko},
     title = {On the asymptotic expansion of {Green's} function for the heat conduction equation with small parameter},
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     volume = {16},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1972_16_2_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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. Bibliography: 5 titles.

[1] M. Kats, Neskolko veroyatnostnykh zadach fiziki i matematiki, Nauka, Moskva, 1967 | Zbl

[2] V. I. Smirnov, Kurs vysshei matematiki, t. IV, Gostekhizdat, Moskva, 1953

[3] R. H. Cameron, “A family of integrals, serving to connect the Wiener and Feynman integrals”, J. Math. Phys., 39 (1960), 126–140 | MR | Zbl

[4] A. Erdeii, Asimptoticheskie razlozheniya, Fizmatgiz, Moskva, 1962

[5] I. G. Petrovskii, Lektsii ob uravneniyakh s chastnymi proizvodnymi, Fizmatgiz, Moskva, 1961 | MR