Contrast Structures in Problems for a Stationary Equation of Reaction-Diffusion-Advection Type with Discontinuous Nonlinearity

被引：13

作者：

Pan, Yafei ^{[1
]}

Ni, Mingkang ^{[1
]}

Davydova, M. A. ^{[2
]}

机构：

[1] East China Normal Univ, Shanghai 200241, Peoples R China

[2] Lomonosov Moscow State Univ, Moscow 119991, Russia

来源：

MATHEMATICAL NOTES | 2018年 / 104卷 / 5-6期

基金：

俄罗斯基础研究基金会; 中国国家自然科学基金;

关键词：

problem of reaction-diffusion-advection type; internal transition layer; asymptotic methods; problems with discontinuous nonlinearity; EXISTENCE; STABILITY;

D O I：

10.1134/S0001434618110159

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A singularly perturbed boundary-value problem for a nonlinear stationary equation of reaction-diffusion-advection type is studied. A new class of problems with discontinuous advective and reactive terms is considered. The existence of contrast structures in problems of this type is proved, and an asymptotic approximation of the solution with an internal transition layer of arbitrary order of accuracy is obtained.

引用

页码：735 / 744

页数：10

共 8 条

[1] Existence and Stability of Contrast Structures in Multidimensional Singularly Perturbed Reaction-Diffusion-Advection Problems [J].

Davydova, M. A. ;

Nefedov, N. N. .

NUMERICAL ANALYSIS AND ITS APPLICATIONS (NAA 2016), 2017, 10187 :277-285

[2] Existence and Stability of Solutions with Boundary Layers in Multidimensional Singularly Perturbed Reaction-Diffusion-Advection Problems [J].

Davydova, M. A. .

MATHEMATICAL NOTES, 2015, 98 (5-6) :909-919

[3] Time-independent reaction-diffusion equation with a discontinuous reactive term [J].

Levashova, N. T. ;

Nefedov, N. N. ;

Orlov, A. O. .

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2017, 57 (05) :854-866

[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., 2015, ZH VYCH MAT MAT FIZ, V55, P2042, DOI 10.7868/S0044466915120133

[6]

Nefedov N. N., 2012, DIFF URAVN, V48, P738

[7]

Vasil'eva A. B., 2010, T MAT I STEKLOVA, P268

[8]

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

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