Geodesic
The Cauchy problem for Tikhonov’s system in the case of a multiple root of the degenerate equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 1, pp. 34-45 
M. V. Butuzova. The Cauchy problem for Tikhonov’s system in the case of a multiple root of the degenerate equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 1, pp. 34-45. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_1_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For a system of the Tikhonov type in the case of a double root of the degenerate equation, the asymptotics of the boundary-layer solution is constructed and justified. The character of the asymptotics and the algorithm for constructing it differ substantially from the classical case when the degenerate equation has a simple root.

[1] Tikhonov A. N., “Sistemy differentsialnykh uravnenii, soderzhaschie malye parametry”, Matem. sbornik, 31(73):3 (1952), 147–156

[2] Vasileva A. B., Butuzov V. F., Asimptoticheskie razlozheniya reshenii singulyarno vozmuschennykh uravnenii, Nauka, M., 1973

[3] Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989

[4] Butuzov V. F., “Ob osobennostyakh pogranichnogo sloya v singulyarno vozmuschennykh zadachakh s kratnym kornem vyrozhdennogo uravneniya”, Matem. zametki, 94:1 (2013), 68–80 | DOI