Geodesic
An~estimate of solutions of parabolic problems without an initial condition
Izvestiya. Mathematics , Tome 38 (1992) no. 2, pp. 429-433.

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A solution of a parabolic equation without an initial condition is determined in terms of the right side in a semi-infinite cylinder. It is assumed that the coefficients of the equation do not depend on time. An estimate of the solution is given in terms of the right side of the equation, which estimate contains a weighted exponential function of time. 
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Yu. P. Krasovskii. An~estimate of solutions of parabolic problems without an initial condition. Izvestiya. Mathematics , Tome 38 (1992) no. 2, pp. 429-433. http://geodesic.mathdoc.fr/item/IM2_1992_38_2_a10/

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[2] Mizokhata S., Teoriya uravnenii s chastnymi proizvodnymi, Mir, M., 1977

[3] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1972 | MR