Geodesic
Justification of asymptotic decomposition of a solution for the problem of the motion of weak solutions of polymers near a critical point
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 313-317.

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

We consider the boundary-value problem in a semibounded interval for a third-order integro-differential equation with the small parameter multiplies the product of the integral of unknown function vanishing on the boundary and its highest derivative. Such a problem arises in the description of the motion of weak solutions of polymers near a critical point. Unique solvability for the problem for all values of the parameter in [0,1] is proved in [1]. In this paper the representation of a solution as an asymptotic series in non-negative integer powers of the small parameter is established.
Keywords: flow of an aqueous solution of polymers, boundary-value problem in a semibounded interval, small parameter, asymptotic solution. 
@article{SEMR_2020_17_a85,
     author = {A. G. Petrova},
     title = {Justification of asymptotic decomposition of a solution for the problem of the motion of weak solutions of polymers near a critical point},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {313--317},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a85/}
}
TY  - JOUR
AU  - A. G. Petrova
TI  - Justification of asymptotic decomposition of a solution for the problem of the motion of weak solutions of polymers near a critical point
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2020
SP  - 313
EP  - 317
VL  - 17
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2020_17_a85/
LA  - ru
ID  - SEMR_2020_17_a85
ER  - 
%0 Journal Article
%A A. G. Petrova
%T Justification of asymptotic decomposition of a solution for the problem of the motion of weak solutions of polymers near a critical point
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2020
%P 313-317
%V 17
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2020_17_a85/
%G ru
%F SEMR_2020_17_a85
A. G. Petrova. Justification of asymptotic decomposition of a solution for the problem of the motion of weak solutions of polymers near a critical point. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 313-317. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a85/

[1] A.G. Petrova, “On the Unique Solvability of the Problem of the Flow of an Aqueous Solution of Polymers near a Critical Point”, Mathematical Notes, 106:5 (2019), 91–100 | MR

[2] V.A. Pavlovskii, “On theoretical description of weak aqueous solutions of polymers”, Dokl. Akad. Nauk SSSR, 200:4 (1971), 809–812

[3] T.P. Pukhnacheva, “The problem of the axially symmetric flow of an aqueous solution of polymers near a critical point”, Trudy Sem. Geom. i Mat. Model., 2, Altai Gos. Univ., Barnaul, 2016, 75–80 (in Russian)

[4] A.V. Pechkurov, “On invertibility in the Schwartz space of the operator generated by a tempered pencil”, Vestn. Voronezh. Gos. Univ., Ser. Fiz. Mat., 2 (2011), 122–128 | Zbl

[5] L.A. Lusternik, V.J. Sobolev, Elements of Functional Analysis, Frederick Ungar Publishing Company, Constable and Co., New York–London, 1961 | MR | Zbl

[6] A.G. Petrova, V.V. Pukhnachev, O.A. Frolovskaya, “Analytical and numerical investigation of unsteady flow near a critical point”, J. Appl. Math. Mech., 80:3 (2016), 215–224 | MR | Zbl