Geodesic
On a singularly perturbed mixed problem for a linear parabolic equation with nonlinear boundary conditions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 1, pp. 80-88 
A. A. Belolipetskii; A. M. Ter-Krikorov. On a singularly perturbed mixed problem for a linear parabolic equation with nonlinear boundary conditions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 1, pp. 80-88. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_1_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A mixed problem for a linear parabolic equation with a small parameter multiplying the time derivative and with nonlinear boundary conditions is solved. Such boundary conditions arise in some heat and mass transfer problems, for example, in cooling thin spherical gas-filled shells or in the case of a gas filling such shells with gas-permeable walls.

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[2] Belolipetskii A. A., “Matematicheskoe modelirovanie protsessa desublimatsii izotopov vodoroda v lazernoi misheni”, Tr. MFTI, 1:4 (2009), 7–22

[3] Belolipetskii A. A., Semenov K. O., “Issledovanie matematicheskoi modeli zapolneniya dvukhsloinykh poristykh obolochek gazom”, Vestnik MGU. Ser. 15. Vychisl. matem. i kibernetika, 2011, no. 4, 3–10 | MR

[4] Vasileva A. B., Butuzov V. F., Asimptoticheskie metody v teorii singulyarnykh vozmuschenii, Vysshaya shkola, M., 1990 | MR

[5] Ter-Krikorov A. M., Nelineinyi analiz i asimptoticheskie metody malogo parametra, Uchebnoe posobie, MFTI, M., 2007

[6] Belolipetskii A. A., Ter-Krikorov A. M., “O reshenii odnoi singulyarno vozmuschennoi nachalno-kraevoi zadachi dlya lineinogo parabolicheskogo uravneniya”, Tr. MFTI, 3:1 (2011), 14–17 | MR