Original Paper

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

  • Qunyi BieAffiliated withSchool of Mathematics and Computational Science, Sun Yat-Sen UniversityCollege of Science, China Three Gorges University
  • , Qiru WangAffiliated withSchool of Mathematics and Computational Science, Sun Yat-Sen University Email author 

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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