Geodesic
Singularly perturbed boundary value problem with multizonal interior transitional layer
Modelirovanie i analiz informacionnyh sistem, Tome 22 (2015) no. 1, pp. 5-22.

Voir la notice de l'article provenant de la source Math-Net.Ru

Two-point boundary value problem for a singularly perturbed ordinary differential equation of second order is considered in the case when the degenerate equation has three unintersecting roots from which one root is two-tuple and two roots are one-tuple. It is prooved that for sufficiently small values of the small parameter the problem has a solution with the transition from the two-tuple root of the degenerate equation to the one-tuple root in the neighbourhood of an internal point of the interval. The asymptotic expansion of this solution is constructed. It distinguishes from the known expansion in the case when all roots of the degenerate equation are one-tuple, in particular, the transitional layer is multizonal.
Keywords: singularly perturbed equation, interior transitional layer, asymptotic expansion of solution. 
@article{MAIS_2015_22_1_a0,
     author = {V. F. Butuzov},
     title = {Singularly perturbed boundary value problem  with multizonal interior transitional layer},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {5--22},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2015_22_1_a0/}
}
TY  - JOUR
AU  - V. F. Butuzov
TI  - Singularly perturbed boundary value problem  with multizonal interior transitional layer
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2015
SP  - 5
EP  - 22
VL  - 22
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2015_22_1_a0/
LA  - ru
ID  - MAIS_2015_22_1_a0
ER  - 
%0 Journal Article
%A V. F. Butuzov
%T Singularly perturbed boundary value problem  with multizonal interior transitional layer
%J Modelirovanie i analiz informacionnyh sistem
%D 2015
%P 5-22
%V 22
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2015_22_1_a0/
%G ru
%F MAIS_2015_22_1_a0
V. F. Butuzov. Singularly perturbed boundary value problem  with multizonal interior transitional layer. Modelirovanie i analiz informacionnyh sistem, Tome 22 (2015) no. 1, pp. 5-22. http://geodesic.mathdoc.fr/item/MAIS_2015_22_1_a0/

[1] Vasilieva A. B., Butuzov V. F., Asimptoticheskiye metody v teorii singulyarnyh vozmusheniy, Vysshaya shkola, M., 1990 (in Russian)

[2] V. F. Butuzov, “On the Special Properties of the Boundary Layer in Singularly Perturbed Problems with Multiple Root of the Degenerate Equation”, Mathematical Notes, 94:1 (2013), 60–70 | DOI | DOI

[3] V. F. Butuzov, “On periodic solutions to singularly perturbed parabolic problems in the case of multiple roots of the degenerate equation”, Computational Mathematics and Mathematical Physics, 51:1 (2011), 40–50 | DOI

[4] Vasilieva A. B., Butuzov V. F., Asimptoticheskiye razlozheniya resheniy singulyarno vozmushchennykh uravneniy, Nauka, M., 1973 (in Russian)