Abstract:
The paper proposes an analogue of Vishik–Lyusternik–Vasileva–Imanalieva boundary functions method for constructing a uniform asymptotic expansion of solutions to bisingular perturbed problems. By means of this method we construct the uniform asymptotic expansion for the solution to the Dirichlet problem for bisingular perturbed second order elliptic equation with two independent variables in a circle. By the maximum principle we justify formal asymptotic expansion of the solution, that is, an estimate for the error term is established.
Citation:
D. A. Tursunov, U. Z. Erkebaev, “Asymptotic expansions of solutions to Dirichlet problem for elliptic equation with singularities”, Ufa Math. J., 8:1 (2016), 97–107
\Bibitem{TurErk16}
\by D.~A.~Tursunov, U.~Z.~Erkebaev
\paper Asymptotic expansions of solutions to Dirichlet problem for elliptic equation with singularities
\jour Ufa Math. J.
\yr 2016
\vol 8
\issue 1
\pages 97--107
\mathnet{http://mi.mathnet.ru/eng/ufa320}
\crossref{https://doi.org/10.13108/2016-8-1-97}
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Linking options:
https://www.mathnet.ru/eng/ufa320
https://doi.org/10.13108/2016-8-1-97
https://www.mathnet.ru/eng/ufa/v8/i1/p102
This publication is cited in the following 10 articles:
D. A. Tursunov, M. O. Orozov, A. A. Halmatov, “Asymptotics of the solution to the boundary-value problems with non smooth coefficient”, Lobachevskii J. Math., 41:6, SI (2020), 1115–1122
D. A. Tursunov, M. O. Orozov, “Asymptotics of the solution to the roben problem for a ring with regularly singular boundary”, Lobachevskii J. Math., 41:1, SI (2020), 89–95
K. G. Kozhobekov, U. Z. Erkebaev, D. A. Tursunov, “Asymptotics of the solution to the boundary-value problems when limited equation has singular point”, Lobachevskii J. Math., 41:1, SI (2020), 96–101
D. A. Tursunov, M. O. Orozov, “Asimptoticheskoe reshenie vozmuschennoi pervoi kraevoi zadachi s negladkim koeffitsientom”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 12:3 (2020), 41–47
D. A. Tursunov, “Asymptotic solving linear bisingular problems with additional boundary layer”, Russian Math. (Iz. VUZ), 62:3 (2018), 60–67
D. A. Tursunov, “Asimptotika resheniya zadachi Dirikhle s singulyarnostyu vnutri koltsa”, Matematicheskaya fizika i kompyuternoe modelirovanie, 21:1 (2018), 44–52
D. A. Tursunov, E. A. Tursunov, “Asimptotika resheniya bisingulyarnoi zadachi Koshi dlya sistem obyknovennykh differentsialnykh uravnenii”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2017, no. 1(38), 33–41
D. A. Tursunov, “Obobschennyi metod pogranfunktsii dlya bisingulyarnykh zadach v kruge”, Tr. IMM UrO RAN, 23, no. 2, 2017, 239–249
D. A. Tursunov, “The Asymptotic Solution of the Three-Band Bisingularly Problem”, Lobachevskii J. Math., 38:3, SI (2017), 542–546
D. A. Tursunov, U. Z. Erkebaev, E. A. Tursunov, “Asimptotika resheniya zadachi Dirikhle dlya koltsa s kvadratichnymi rostami na granitsakh”, Izv. IMI UdGU, 2016, no. 2(48), 73–81
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