Contrast structures in the reaction-diffusion-advection equations in the case of balanced advection

被引：7

作者：

Levashova, N. T. ^{[1
]}

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

Yagremtsev, A. V. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Dept Phys, Moscow 119992, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2013年 / 53卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

singularly perturbed parabolic problems; reaction-diffusion equations; internal layers; asymptotic methods; method of differential inequalities; Lyapunov stability;

D O I：

10.1134/S096554251303007X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a singularly perturbed parabolic equation termed in applications as the reaction-diffusion-advection equation, stationary solutions with internal transition layers (contrast structures) are studied. An arbitrary-order asymptotic approximation of such solutions is constructed, and an existence theorem is proved. An efficient algorithm for constructing an asymptotic approximation of the transition point is proposed. The constructed asymptotic approximation is justified by applying the asymptotic method of differential inequalities, which is extended to the class of problems under study. This method is also used to establish the Lyapunov stability of such stationary solutions. DOI: 10.1134/S096554251303007X

引用

页码：273 / 283

页数：11

共 50 条

[1] Contrast structures in the reaction-diffusion-advection equations in the case of balanced advection
N. T. Levashova
N. N. Nefedov
A. V. Yagremtsev
[J]. Computational Mathematics and Mathematical Physics, 2013, 53 : 273 - 283
[2] Contrast structures in singularly perturbed quasilinear reaction-diffusion-advection equations
N. N. Nefedov
M. A. Davydova
[J]. Differential Equations, 2013, 49 : 688 - 706
[3] Contrast structures in singularly perturbed quasilinear reaction-diffusion-advection equations
Nefedov, N. N.
Davydova, M. A.
[J]. DIFFERENTIAL EQUATIONS, 2013, 49 (06) : 688 - 706
[4] Contrast Structures in the Reaction-Diffusion-Advection Problem in the Case of a Weak Reaction Discontinuity
Nefedov, N. N.
Nikulin, E., I
Orlov, A. O.
[J]. RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, 2022, 29 (01) : 81 - 90
[5] Contrast Structures in the Reaction-Diffusion-Advection Problem in the Case of a Weak Reaction Discontinuity
N. N. Nefedov
E. I. Nikulin
A. O. Orlov
[J]. Russian Journal of Mathematical Physics, 2022, 29 : 81 - 90
[6] Periodic contrast structures in systems of the reaction-diffusion-advection type
N. N. Nefedov
M. A. Davydova
[J]. Differential Equations, 2010, 46 : 1309 - 1321
[7] Periodic Contrast Structures in Systems of the Reaction-Diffusion-Advection Type
Nefedov, N. N.
Davydova, M. A.
[J]. DIFFERENTIAL EQUATIONS, 2010, 46 (09) : 1309 - 1321
[8] Existence of a solution in the form of a moving front of a reaction-diffusion-advection problem in the case of balanced advection
Levashova, N. T.
Nefedov, N. N.
Yagremtsev, A., V
[J]. IZVESTIYA MATHEMATICS, 2018, 82 (05) : 984 - 1005
[9] Contrast structures in multidimensional singularly perturbed reaction-diffusion-advection problems
Nefedov, N. N.
Davydova, M. A.
[J]. DIFFERENTIAL EQUATIONS, 2012, 48 (05) : 745 - 755
[10] Contrast structures in multidimensional singularly perturbed reaction-diffusion-advection problems
N. N. Nefedov
M. A. Davydova
[J]. Differential Equations, 2012, 48 : 745 - 755

← 1 2 3 4 5 →