APPROXIMATE-ASYMPTOTIC SOLUTION OF A SINGULARLY PERTURBATED FIRST BOUNDARY VALUE PROBLEM FOR A RING
DOI:
https://doi.org/10.52754/16948645_2022_1_5Keywords:
singular perturbation, first boundary value problem, elliptic type equation, Vishik-Lyusternik method, Laplacian, potentialAbstract
In this paper, we consider an inhomogeneous first boundary value problem, i.e. the Dirichlet problem in rings for a linear inhomogeneous second-order elliptic equation with two independent variables containing a small parameter in front of the Laplacian. The potential of the equation is a smooth function in the annulus. We are interested in the influence of a small parameter on the solution of the Dirichlet problem in a ring, as the small parameter tends to zero from the right. To construct an approximately asymptotic solution, we use the Vishik-Lyusternik method. As a result, we have constructed a uniform asymptotic expansion of the solution of the first boundary value problem in a ring in a small parameter up to the second order of accuracy in a small parameter. The rate of convergence of the remainder term to zero for small values of the small parameter is indicated.
References
Бутузов, В. Ф. Асимптотика и устойчивость решения сингулярно возму-щенной эллиптической задачи с трехкратным корнем вырожденного урав-нения // Изв. РАН. Сер. матем. –2017. – Т. 81. – Вып. 3. – C. 21–44. DOI: https://doi.org/10.4213/im8478
Зайцев, А. Б. О принципе максимума для решений эллиптических уравнений второго порядка // Изв. вузов. Матем. –2020. – № 8. – С. 11–17. DOI: https://doi.org/10.26907/0021-3446-2020-8-11-17
Tursunov D. A., Orozov М.О., Кhalmatov А.А. Asymptotics of the Solution to the Boundary-Value Problems with Non Smooth Coefficient // Lobachevskii Journal of Mathematics. – 2020. – Vol. 41. – No. 6. –P. 1115-1122. DOI: https://doi.org/10.1134/S1995080220060177
Khalmatov, A. A. Analysis of finding a solution to modular equations when the equation contains two or more modules / A. A. Khalmatov, G. A. Dadazhanova, K. A. Abbazova, N. Sayfiddin K // Science. Education. Engineering. – 2022. – No. 3(75). – P. 49-57. – DOI 10.54834/16945220_2022_3_49. – EDN JQQTXH. DOI: https://doi.org/10.54834/16945220_2022_3_49
Khalmatov, A. A. Spice of solutions to singularly perturbed equations / A. A. Khalmatov, K. A. Abbazova, G. Kanybek K, A. Baltabaev // Science. Education. Engineering. – 2022. – No. 3(75). – P. 57-63. – DOI 10.54834/16945220_2022_3_57. – EDN QCRAZR. DOI: https://doi.org/10.54834/16945220_2022_3_57
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Journal of Osh State University. Mathematics. Physics. Technical Science
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
