Asymptotic behaviour of the solution to a singularly perturbed partially dissipative system with a multiple root of the degenerate equation

被引：7

作者：

Butuzov, V. F. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Fac Phys, Moscow, Russia

来源：

SBORNIK MATHEMATICS | 2016年 / 207卷 / 08期

基金：

俄罗斯基础研究基金会;

关键词：

singularly perturbed problem with a multiple root of the degenerate equation; boundary layer; partially dissipative system; BOUNDARY-VALUE-PROBLEM;

D O I：

10.1070/SM8602

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Asymptotic formulae for the solution of the initial-boundary value problem for a singularly perturbed partially dissipative system of reaction-diffusion type are constructed and justified. The system consists of a parabolic and an ordinary differential equation in the case when the corresponding degenerate equation has a root of multiplicity two. The behaviour of the boundary layer functions and the algorithm for constructing them are significantly distinct from the case of a simple (multiplicity-one) root of the degenerate equation.

引用

页码：1100 / 1126

页数：27

共 8 条

[1] Asymptotics of the solution of an initial-boundary value problem for a singularly perturbed parabolic equation in the case of double root of the degenerate equation [J].

Butuzov, V. F. ;

Bychkov, A. I. .

DIFFERENTIAL EQUATIONS, 2013, 49 (10) :1261-1273

[2] On the special properties of the boundary layer in singularly perturbed problems with multiple root of the degenerate equation [J].

Butuzov, V. F. .

MATHEMATICAL NOTES, 2013, 94 (1-2) :60-70

[3] PARTLY DISSIPATIVE REACTION-DIFFUSION SYSTEMS AND A MODEL OF PHOSPHORUS DIFFUSION IN SILICON [J].

HOLLIS, SL ;

MORGAN, JJ .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1992, 19 (05) :427-440

[4]

Ilin A.M., 1989, Matching of asymptotic expansions of solations of boundary value problems

[5]

NEFEDOV NN, 1995, DIFF URAVN, V31, P719

[6]

Pao C. V., 2004, Nonlinear Parabolic and Elliptic Equations, DOI DOI 10.1007/978-1-4615-3034-3

[7] Boundary layers in the solution of singularly perturbed boundary value problem with a degenerate equation having roots of multiplicity two [J].

Vasil'eva, A. B. .

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2011, 51 (03) :351-354

[8]

Vasileva A. B., 1990, Asymptotic Methods in the Theory of Singular Perturbations

← 1 →