Journal of Mathematical Chemistry

, Volume 43, Issue 3, pp 1134–1140 | Cite as

Stability of solutions to a reaction diffusion system based upon chemical reaction kinetics


In this paper, we deal with the stability problem to some mathematical models that describe chemical reaction kinetics. One is a set of ordinary differential equations induced by one reversible chemical reaction mechanism containing three chemical species. The other is a set of reaction diffusion equations based on the same chemical reaction. We show that all solutions of the model are asymptotically stable by applying the Liapunov method. We thus find that the concentration of each species has certain limits as time proceeds.


reaction diffusion system Liapunov stability 

subject classification

34D20 34D23 35K57 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chen W., Li C., Wright E.S. (2005) . Commun. Pure Appl. Anal. 4: 889–899Google Scholar
  2. 2.
    Evans L.C. (2002) Partial Differential Equations. AMS, Rhode IslandGoogle Scholar
  3. 3.
    Hale J.K. (1969) Ordinary Differential Equations. Wiley, New YorkGoogle Scholar
  4. 4.
    Li C., Wright E.S. (2001) . Discrete Contin. Dyn. Syst. 7(2): 377–384CrossRefGoogle Scholar
  5. 5.
    Li C., Wright E.S. (2002) . Commun. Pure Appl. Anal. 1: 77–84Google Scholar
  6. 6.
    R.H. Petrucci, General Chemistry (New York, 1982), p. 440.Google Scholar
  7. 7.
    Toth J., Li G., Rabitz H., Tomlin A.S. (1997) . Siam J. Appl. Math. 57: 1531–1556CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Applied Mathematics, 526 UCBUniversity of Colorado at BoulderBoulderUSA

Personalised recommendations