Geodesic
Asymptotic behaviour of the solution of the singularly perturbed parabolic problem in the critical case
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 6, pp. 858-867 
V. Yu. Buchnev. Asymptotic behaviour of the solution of the singularly perturbed parabolic problem in the critical case. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 6, pp. 858-867. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_6_a5/
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     title = {Asymptotic behaviour of the solution of the singularly perturbed parabolic problem in the critical case},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A zeroth-order boundary-layer asymptotic expansion is constructed and proved for solving a mixed boundary-value problem for a parabolic equation in the critical case. A smoothing procedure is applied to the nonsmooth terms of the asymptotic expansion when constructing the solution.

[1] Zino I. E., Tropp E. A., Asimptoticheskie metody v zadachakh teorii teploprovodnosti i termouprugosti, Izd-vo LGU, L., 1978

[2] Vasileva A. B., Butuzov V. F., Singulyarno vozmuschennye uravneniya v kriticheskikh sluchayakh, Izd-vo MGU, M., 1978 | MR

[3] Butuzov V. F., Nesterov A. V., “Ob asimptotike resheniya uravneniya parabolicheskogo tipa s malymi parametrami pri starshikh proizvodnykh”, Zh. vychisl. matem. i matem. fiz., 22:4 (1982), 865–870 | MR | Zbl