Geodesic
Asymptotics of the Dirichlet problem solution for a ring with quadratic growths on the boundaries
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 48 (2016) no. 2, pp. 73-81

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

The paper refers to the asymptotic behavior of the Dirichlet bisingular problem solution for a ring with quadratic growths on the boundaries. To construct the asymptotic expansion of the solution the authors apply the modified scheme of the classical method of boundary functions. The proposed method differs from the matching method by the fact that growing features of the outer expansion are in fact removed from it and with the help of an auxiliary asymptotic series are placed entirely in the internal expansion. An asymptotic expansion of the solution is a series of Puiseux, the basic term of the asymptotic expansion of the solution has a negative fractional degree of the small parameter. The resulting asymptotic expansion of the Dirichlet problem solution is justified by the maximum principle.
Keywords: asymptotic expansion of solution, Dirichlet problem, small parameter, method of boundary functions.
Mots-clés : bisingular perturbation, Puiseux series 
@article{IIMI_2016_48_2_a5,
     author = {D. A. Tursunov and U. Z. Erkebaev and E. A. Tursunov},
     title = {Asymptotics of the {Dirichlet} problem solution for a ring with quadratic growths on the boundaries},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {73--81},
     publisher = {mathdoc},
     volume = {48},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2016_48_2_a5/}
}
TY  - JOUR
AU  - D. A. Tursunov
AU  - U. Z. Erkebaev
AU  - E. A. Tursunov
TI  - Asymptotics of the Dirichlet problem solution for a ring with quadratic growths on the boundaries
JO  - Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
PY  - 2016
SP  - 73
EP  - 81
VL  - 48
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IIMI_2016_48_2_a5/
LA  - ru
ID  - IIMI_2016_48_2_a5
ER  - 
%0 Journal Article
%A D. A. Tursunov
%A U. Z. Erkebaev
%A E. A. Tursunov
%T Asymptotics of the Dirichlet problem solution for a ring with quadratic growths on the boundaries
%J Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
%D 2016
%P 73-81
%V 48
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IIMI_2016_48_2_a5/
%G ru
%F IIMI_2016_48_2_a5
D. A. Tursunov; U. Z. Erkebaev; E. A. Tursunov. Asymptotics of the Dirichlet problem solution for a ring with quadratic growths on the boundaries. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 48 (2016) no. 2, pp. 73-81. http://geodesic.mathdoc.fr/item/IIMI_2016_48_2_a5/