Existence and Stability of Periodic Contrast Structures in the Reaction-Advection-Diffusion Problem

被引：20

作者：

Nefedov, N. N. ^{[1
]}

Nikulin, E. I. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Dept Phys, Dept Math, Moscow 119991, Russia

来源：

RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS | 2015年 / 22卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

SINGULARLY PERTURBED PROBLEMS; DIFFERENTIAL-INEQUALITIES; INTERNAL LAYERS;

D O I：

10.1134/S1061920815020089

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A singularly perturbed periodic problem for a parabolic reaction-advection-diffusion equation at low advection is studied. The case when there is an internal transition layer under unbalanced nonlinearity is considered. An asymptotic expansion of a solution is constructed. To substantiate the asymptotics thus constructed, the asymptotic method of differential inequalities is used. The Lyapunov asymptotic stability of a periodic solution is studied; the proof uses the Krein-Rutman theorem.

引用

页码：215 / 226

页数：12

共 15 条

[1]

Amman H., 1978, PERIODIC SOLUTIONS S

[2] Front Motion in the Parabolic Reaction-Diffusion Problem [J].

Bozhevol'nov, Yu. V. ;

Nefedov, N. N. .

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2010, 50 (02) :264-273

[3]

Hess P., 1991, Periodic-Parabolic Boundary Value Problems and Positivity

[4] Existence and asymptotic stability of periodic solutions with an interior layer of reaction-advection-diffusion equations [J].

Nefedov, N. N. ;

Recke, L. ;

Schneider, K. R. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 405 (01) :90-103

[5]

Nefedov N. N., 2000, Differ. Equations, V36, P262, DOI [10.1007/BF02754216, DOI 10.1007/BF02754216]

[6]

Nefedov N, 2013, LECT NOTES COMPUT SC, V8236, P62, DOI 10.1007/978-3-642-41515-9_6

[7] An asymptotic method of differential inequalities for the investigation of periodic contrast structures: Existence, asymptotics, and stability [J].

Nefedov, NN .

DIFFERENTIAL EQUATIONS, 2000, 36 (02) :298-305

[8]

Nefedov NN, 1995, DIFF EQUAT+, V31, P1077

[9]

Pao CV., 1992, NONLINEAR PARABOLIC, DOI DOI 10.1007/978-1-4615-3034-3

[10] Singularly perturbed problems with boundary and internal layers [J].

Vasil'eva, A. B. ;

Butuzov, V. F. ;

Nefedov, N. N. .

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2010, 268 (01) :258-273

← 1 2 →