Geodesic
An estimate of solutions of parabolic problems without an initial condition
Izvestiya. Mathematics, Tome 38 (1992) no. 2, pp. 429-433 
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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     title = {An~estimate of solutions of parabolic problems without an initial condition},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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[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