Journal of Mathematical Chemistry

, Volume 51, Issue 2, pp 637–659

Stationary patterns in a two-cell coupled isothermal chemical system with arbitrary powers of autocatalysis

Original Paper

DOI: 10.1007/s10910-012-0111-x

Cite this article as:
Bie, Q. & Wang, Q. J Math Chem (2013) 51: 637. doi:10.1007/s10910-012-0111-x

Abstract

Stationary patterns of a two-cell coupled isothermal chemical system with arbitrary powers of autocatalysis are considered. Firstly, we obtain the stability of the unique positive constant equilibrium solution for the system. Then, based on a priori estimates, non-existence and existence of nontrivial steady state solutions are shown by using implicit function theorem and topological degree theory, respectively. The effects of autocatalysis order and diffusion coefficients to the pattern formation are discussed.

Keywords

Autocatalytic chemical system Arbitrary powers of autocatalysis Leray–Schauder degree Pattern 

Mathematics Subject Classification (2010)

35K57 35K55 

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.School of Mathematics and Computational ScienceSun Yat-Sen UniversityGuangzhouPeople’s Republic of China
  2. 2.College of ScienceChina Three Gorges UniversityYichangPeople’s Republic of China

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