Asymptotic step-like solutions of the singularly perturbed Burgers equation

被引：0

作者：

Samoilenko, V. ^{[1
]}

Samoilenko, Yu. ^{[2
]}

Zappale, E. ^{[3
]}

机构：

[1] Taras Shevchenko Natl Univ Kyiv, Dept Math Phys, Vul Volodymyrska 60, UA-01033 Kiev, Ukraine

[2] Claude Bernard Lyon 1 Univ, Inst Camille Jordan, Ave Claude Bernard 21,Batiment Braconnier, F-69622 Lyon, France

[3] Sapienza Univ Rome, Dept Basic & Appl Sci Engn, Via Antonio Scarpa 16, I-00161 Rome, Italy

来源：

PHYSICS OF FLUIDS | 2023年 / 35卷 / 06期

关键词：

921.2 Calculus - 931 Classical Physics; Quantum Theory; Relativity;

D O I：

10.1063/5.0150685

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

This paper deals with a problem of asymptotic step-like solutions of the Burgers equation with variable coefficients and a small parameter. By means of the nonlinear Wentzel-Kramers-Brillouin method, the algorithm of constructing these asymptotic solutions is proposed and statements on justification of the algorithm are proved. The obtained results are illustrated by an example, for which the first asymptotic step-like approximation is explicitly found. The asymptotic solution is global and has a form of the shock wave type function. There are also given graphs of these approximate solutions for certain numerical parameters.

引用

页数：9

共 50 条

[1] Periodic step-like contrast structures for a singularly perturbed parabolic equation
A. B. Vasil’eva
O. E. Omel’chenko
Differential Equations, 2000, 36 : 236 - 246
[2] Periodic step-like contrast structures for a singularly perturbed parabolic equation
Vasil'eva, AB
Omel'chenko, OE
DIFFERENTIAL EQUATIONS, 2000, 36 (02) : 236 - 246
[3] On Step-Like Contrast Structure of Singularly Perturbed Systems
Ni, Mingkang
Wang, Zhiming
BOUNDARY VALUE PROBLEMS, 2009,
[4] On Step-Like Contrast Structure of Singularly Perturbed Systems
Mingkang Ni
Zhiming Wang
Boundary Value Problems, 2009
[5] Asymptotic analysis of solutions of singularly perturbed equation
Ma, HK
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON DIFFERENTIAL EQUATIONS AND COMPUTATIONAL SIMULATIONS, 2000, : 265 - 269
[6] STEP-LIKE CONTRASTING STRUCTURES FOR A SYSTEM OF SINGULARLY PERTURBED EQUATIONS
VASILYEVA, AB
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 1994, 34 (10) : 1215 - 1223
[7] Step-like contrast structure in a singularly perturbed system of parabolic equations
N. T. Levashova
A. A. Mel’nikova
Differential Equations, 2015, 51 : 342 - 361
[8] Step-like contrast structure in a singularly perturbed system of parabolic equations
Levashova, N. T.
Mel'nikova, A. A.
DIFFERENTIAL EQUATIONS, 2015, 51 (03) : 342 - 361
[9] STEP-LIKE CONTRAST STRUCTURE OF SINGULARLY PERTURBED OPTIMAL CONTROL PROBLEM
Ni, Mingkang
Wu, Limeng
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2012, 30 (01) : 2 - 13
[10] Step-like Contrast Structure of Singularly Perturbed Optimal Control Problem
Wu, Limeng
Ni, Mingkang
Lu, Haibo
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2011, (46) : 1 - 16

← 1 2 3 4 5 →