Geodesic
Asymptotics as $t\to0$ for solutions of the heat equation in a domain
Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 383-395 
V. A. Kozlov. Asymptotics as $t\to0$ for solutions of the heat equation in a domain. Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 383-395. http://geodesic.mathdoc.fr/item/SM_1989_64_2_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The Dirichlet problem is considered for a second-order parabolic equation in a domain with a conical point on the boundary. The right sides need not satisfy consistency conditions at the initial time. A complete asymptotic expansion as $t\to0$ is obtained; it is uniform with respect to the space variables. Bibliography: 6 titles.

[1] Kondratev V. A., Oleinik O. Ya., “Kraevye zadachi dlya uravnenii s chastnymi proizvodnymi v negladkikh oblastyakh”, UMN, 38:2 (1983), 3–77 | MR

[2] Kondratev V. A., “Kraevye zadachi dlya ellipticheskikh uravnenii v oblastyakh s konicheskimi ili uglovymi tochkami”, Tr. MMO, 16 (1967), 209–292

[3] Beitman G., Erdeii A., Vysshie transtsendentnye funktsii, T. I, Nauka, M., 1965

[4] Kozlov V. A., Mazya V. G., “Ob osobennostyakh reshenii pervoi kraevoi zadachi dlya uravneniya teploprovodnosti v oblastyakh s konicheskimi tochkami. I”, Izv. vuzov. Matematika, 1987, no. 2, 38–47 | MR

[5] Kozlov V. A., Mazya V. G., “Ob osobennostyakh reshenii pervoi kraevoi zadachi dlya uravneniya teploprovodnosti v oblastyakh s konicheskimi tochkami. II”, Izv. vuzov. Matematika, 1987, no. 3, 37–44 | MR | Zbl

[6] Mazya V. G., Plamenevskii B. A., “Ob asimptotike fundamentalnykh reshenii ellipticheskikh kraevykh zadach v oblastyakh s konicheskimi tochkami”, Problemy matem. analiza, 7, LGU, L., 1979, 100–145 | MR