STEADY-STATE SOLUTIONS AND STABILITY FOR A CUBIC AUTOCATALYSIS MODEL

被引：1

作者：

Wei, Mei-Hua ^{[1
]}

Wu, Jian-Hua ^{[1
]}

He, Yin-Nian ^{[2
]}

机构：

[1] Shaanxi Normal Univ, Coll Math & Informat Sci, Xian 710062, Peoples R China

[2] Xi An Jiao Tong Univ, Fac Sci, Xian 710049, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2015年 / 14卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Cubic autocatalysis model; steady state solutions; dynamical stability; Lyapunov-Schmidt procedure; singularity theory; STIRRED TANK REACTOR; QUADRATIC AUTOCATALYSIS; IMPERFECT BIFURCATION; GLOBAL BIFURCATION; SINGULARITY THEORY; CHEMICAL-REACTION; TRAVELING-WAVES; REACTION SCHEME; SYSTEM; DECAY;

D O I：

10.3934/cpaa.2015.14.1147

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A reaction-diffusion system, based on the cubic autocatalytic reaction scheme, with the prescribed concentration boundary conditions is considered. The linear stability of the unique spatially homogeneous steady state solution is discussed in detail to reveal a necessary condition for the bifurcation of this solution. The spatially non-uniform stationary structures, especially bifurcating from the double eigenvalue, are studied by the use of Lyapunov-Schmidt technique and singularity theory. Further information about the multiplicity and stability of the bifurcation solutions are obtained. Numerical examples are presented to support our theoretical results.

引用

页码：1147 / 1167

页数：21

共 31 条

[1]

Abdel-Gawad H. I., 2004, Kyungpook Mathematical Journal, V44, P187

[2] CHAOS IN A SIMPLE 2-PHASE REACTOR [J].

ALHUMAIZI, K ;

ARIS, R .

CHAOS SOLITONS & FRACTALS, 1994, 4 (11) :1985-2014

[3]

[Anonymous], 1971, J. Funct. Anal., DOI [DOI 10.1093/imamat/hxv006, 10.1016/0022-1236(71)90030-9]

[4] Local and global bifurcation results for a semilinear boundary value problem [J].

Brown, K. J. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 239 (02) :296-310

[5]

CHEN LS, 1985, ACTA MATH SCI, V5, P261

[6] Propagation of Local Disturbances in Reaction Diffusion Systems Modeling Quadratic Autocatalysis [J].

Chen, Xinfu ;

Qi, Yuanwei .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2008, 69 (01) :273-282

[7]

Crandall M.G., 1971, J. Funct. Anal., V8, P321

[8] THE APPLICATION OF SINGULARITY THEORY TO ISOTHERMAL AUTOCATALYTIC OPEN SYSTEMS - THE ELEMENTARY SCHEME A+MB = (M+1)B [J].

DANNA, A ;

LIGNOLA, PG ;

SCOTT, SK .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1986, 403 (1825) :341-363

[9]

Elrifai E. A., 2008, FAR E J APPL MATH, V32, P435

[10] Creation of spatial structure by an electric field applied to an ionic cubic autocatalator system [J].

Finlayson, AB ;

Merkin, JH .

JOURNAL OF ENGINEERING MATHEMATICS, 2000, 38 (03) :279-296

← 1 2 3 4 →