Geodesic
On systems of two singularly perturbed quasilinear second-order equations
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 5, pp. 21-28 
A. B. Vasil'eva. On systems of two singularly perturbed quasilinear second-order equations. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 5, pp. 21-28. http://geodesic.mathdoc.fr/item/FPM_2006_12_5_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A system of two quasilinear second-order equations with a small parameter standing by the second derivatives is studied. The cases where the matrix of coefficients of the first derivatives has the following eigenvalues are considered: (a) both of them have negative real parts; (b) they are of opposite sign; (c) one of them is equal to zero. To find a solution and its asymptotics, the initial-value or boundary-value problems are posed depending on the form of these eigenvalues.

[1] Vasileva A. B., “Kontrastnye struktury tipa stupenki v singulyarno vozmuschënnykh differentsialnykh uravneniyakh vtorogo poryadka, lineinogo otnositelno proizvodnykh”, ZhVM i MF, 35:4 (1995), 520–531 | MR

[2] Vasileva A. B., “O sisteme dvukh singulyarno vozmuschënnykh kvazilineinykh uravnenii vtorogo poryadka”, ZhVM i MF, 44:4 (2004), 650–661 | MR

[3] Vasileva A. B., Butuzov V. F., Asimptoticheskie razlozheniya reshenii singulyarno vozmuschënnykh uravnenii, Nauka, M., 1973 | MR

[4] Vasileva A. B., Butuzov V. F., Singulyarno vozmuschënnye uravneniya v kriticheskikh sluchayakh, Izd-vo Mosk. un-ta, M., 1978 | MR