Solutions of the heat equation in domains with singularities
Matematičeskie zametki, Tome 64 (1998) no. 2, pp. 163-179.

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We study the asymptotics of solutions to the Dirichlet problem for the heat equation in time-dependent domains with singular points.
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V. N. Aref'ev; L. A. Bagirov. Solutions of the heat equation in domains with singularities. Matematičeskie zametki, Tome 64 (1998) no. 2, pp. 163-179. http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a0/

[1] Petrovskii I. G., “O reshenii pervoi kraevoi zadachi dlya uravneniya teploprovodnosti”, Uch. zapiski MGU, 1934, no. 2, 55–59 | MR | Zbl

[2] Kohn J. J., Nirenberg L., “Degenerate elliptic-parabolic equations of second order”, Comm. Pure Appl. Math., 20:4 (1967), 797–872 | DOI | MR | Zbl

[3] Kondratev V. A., “Kraevye zadachi dlya parabolicheskikh uravnenii v zamknutykh oblastyakh”, Tr. MMO, 15, URSS, M., 1967, 400–451

[4] Mikhailov V. P., “O zadache Dirikhle dlya parabolicheskogo uravneniya”, Matem. sb., 61 (103):1 (1963), 40–64 | MR

[5] Feigin V. I., “O gladkosti reshenii kraevykh zadach dlya parabolicheskikh i vyrozhdayuschikhsya ellipticheskikh uravnenii”, Matem. sb., 82 (124):4 (8) (1970), 551–573 | MR | Zbl

[6] Oleinik O. A., Radkevich E. V., Uravneniya vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi, Itogi nauki i tekhn. Matem. analiz 1969, VINITI, M., 1971 | MR | Zbl

[7] Ivasishen S. D., “Otsenki funktsii Grina odnorodnoi pervoi kraevoi zadachi dlya parabolicheskogo uravneniya vtorogo poryadka v netsilindricheskoi oblasti”, Ukr. matem. zh., 21:1 (1969), 15–27 | MR | Zbl

[8] Solonnikov V. A., O kraevykh zadachakh dlya lineinykh parabolicheskikh sistem differentsialnykh uravnenii obschego vida, Tr. MIAN, 83, Nauka, M.–L., 1965 | MR

[9] Kozlov V. A., Mazya V. G., “Ob osobennostyakh resheniya pervoi kraevoi zadachi dlya uravneniya teploprovodnosti v oblastyakh s konicheskoi tochkoi”, Izv. vuzov. Matem., 1987, no. 2, 38–46 | Zbl

[10] Doan Van Ngok, “Asimptotika reshenii kraevykh zadach dlya parabolicheskikh uravnenii vtorogo poryadka v okrestnosti uglovoi tochki granitsy”, Vestn. MGU. Ser. 1. Matem., mekh., 1984, no. 1, 34–36 | Zbl

[11] Arefev V. N., Bagirov L. A., “Asimptoticheskoe povedenie reshenii zadachi Dirikhle dlya parabolicheskogo uravneniya v oblastyakh s osobennostyami”, Matem. zametki, 59:1 (1996), 12–23 | MR | Zbl

[12] Arefev V. N., Bagirov L. A., Asimptoticheskoe povedenie reshenii uravneniya diffuzii v oblastyakh s osobennostyami, Preprint No 563, IPM RAN, M., 1996

[13] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, T. 2, Nauka, M., 1974

[14] Bagirov L. A., “Apriornye otsenki, teoremy suschestvovaniya i povedenie na beskonechnosti reshenii kvaziellipticheskikh uravnenii v $\mathbb R^n$”, Matem. sb., 110 (152):4 (12) (1979), 475–492 | MR | Zbl

[15] Agranovich M. S., Vishik M. I., “Ellipticheskie zadachi s parametrom i parabolicheskie zadachi obschego vida”, UMN, 19:3 (1964), 53–161 | MR | Zbl

[16] Blekher P. M., “Ob operatorakh, zavisyaschikh meromorfno ot parametra”, Vestn. MGU. Ser. 1. Matem., mekh., 1969, no. 5, 30–36 | Zbl

[17] Milne A., Proc. Edinburgh Math. Soc., 32 (1914), 2–14 ; 33 (1915), 48–64 | DOI | DOI

[18] Ladyzhenskaya L. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967