Asymptotics of the Solution of Bisingularly Perturbed First Boundary Value Problem

被引：0

作者：

Tursunov, D. A. ^{[1
]}

Kozhobekov, K. G. ^{[1
]}

Shoorukov, A. A. ^{[1
]}

机构：

[1] Osh State Univ, Osh 723500, Kyrgyzstan

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2022年 / 43卷 / 02期

关键词：

singularity segment; partial differential equation of parabolic type; bisingularly problem; singular perturbed; asymptotic; method of boundary layer function; first boundary value problem; small parameter; INTEGRODIFFERENTIAL EQUATION; UNIQUE SOLVABILITY; NUMERICAL-SOLUTION; MODEL; RING;

D O I：

10.1134/S1995080222050250

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The article investigates the first boundary-value problem for a singularly perturbed linear inhomogeneous partial differential equation of the parabolic type on a rectangle with a singularly segment. A uniform asymptotic expansion of the solution of the first boundary value problem with an arbitrary degree of accuracy on the given rectangle is constructed when a small parameter tends to zero. In constructing the complete asymptotic solution of the first boundary-value problem is used the modified method of the boundary functions of Goldenveizer-Vishik-Lyusternik-Vasilyeva-Imanaliev. The asymptotic solution is justified by the maximum principle.

引用

页码：506 / 512

页数：7

共 50 条

[1] Asymptotics of the Solution of Bisingularly Perturbed First Boundary Value Problem
D. A. Tursunov
K. G. Kozhobekov
A. A. Shoorukov
[J]. Lobachevskii Journal of Mathematics, 2022, 43 : 506 - 512
[2] On the boundary layer part of the asymptotics of the solution of a singularly perturbed boundary value problem
Zhumanazarova, Assiya
Cho, Young Im
[J]. PROCEEDINGS OF THE 2021 INTERNATIONAL CONFERENCE ON ARTIFICIAL LIFE AND ROBOTICS (ICAROB 2021), 2021, : P48 - P48
[3] Regularized Asymptotics of the Solution of the Singularly Perturbed First Boundary Value Problem on the Semiaxis for a Parabolic Equation with a Rational "Simple" Turning Point
Yeliseev, Alexander
Ratnikova, Tatiana
Shaposhnikova, Daria
[J]. MATHEMATICS, 2021, 9 (04) : 1 - 14
[4] ON ASYMPTOTICS OF THE SOLUTION OF A BOUNDARY VALUE PROBLEM FOR SINGULARLY PERTURBED QUASILINEAR ELLIPTIC EQUATION IN SEMI-INFINITE STRIP
Sabzaliyev, Mahir M.
[J]. PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, 2010, 32 (40): : 175 - 188
[5] A uniform asymptotics of a solution to the boundary value problem for a singularly perturbed second-order equation with a weak singularity
Alymkulov, K
Zupukarov, AZ
[J]. DOKLADY MATHEMATICS, 2004, 70 (02) : 747 - 750
[6] Asymptotics of the solution to an initial boundary value problem for a singularly perturbed parabolic equation in the case of a triple root of the degenerate equation
Butuzov, V. F.
Bychkov, A. I.
[J]. COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2016, 56 (04) : 593 - 611
[7] Asymptotics of the solution to an initial boundary value problem for a singularly perturbed parabolic equation in the case of a triple root of the degenerate equation
V. F. Butuzov
A. I. Bychkov
[J]. Computational Mathematics and Mathematical Physics, 2016, 56 : 593 - 611
[8] On the Construction of Asymptotics of the Solution of Multipoint Boundary-Value Problem for a Linear Degenerate Singularly Perturbed System of Differential Equations
Vira M.B.
[J]. Journal of Mathematical Sciences, 2016, 217 (4) : 385 - 398
[9] Asymptotic convergence of the solution for singularly perturbed boundary value problem with boundary jumps
Mirzakulova, A. E.
Atakhan, N.
Asset, N.
Rysbek, A.
[J]. BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2018, 92 (04): : 64 - 71
[10] ASYMPTOTIC EXPANSION OF THE SOLUTION FOR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM WITH BOUNDARY JUMPS
Erkomekovna, Mirzakulova Aziza
Kudaibergenovich, Dauylbayev Muratkhan
[J]. MISKOLC MATHEMATICAL NOTES, 2023, 24 (01) : 309 - 324

← 1 2 3 4 5 →