Geodesic
Asymptotics around the degeneration spot of heat equation solution with strong degeneration
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 1, pp. 9-19.

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The paper deals with heat equation with strong degeneration. It is known that for such problems initial conditions are not stated at $t=0$ as there exists the only smooth solution of such equation. The paper investigates a class of uniqueness of the solution and studies solvability of the problem in spaces of continuous functions. An asymptotic representation of solution around the degeneration spot is built, i.e. the main part of the solution is defined at $t\to+0$ and residuals are estimated. 
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A. V. Glushko; A. D. Baev; D. S. Shumeeva. Asymptotics around the degeneration spot of heat equation solution with strong degeneration. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 1, pp. 9-19. http://geodesic.mathdoc.fr/item/ISU_2011_11_1_a1/

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[2] Vladimirov V. S., Uravneniya matematicheskoi fiziki, Nauka, M., 1976, 527 pp.