Journal of Mathematical Chemistry

, Volume 42, Issue 4, pp 1135–1145 | Cite as

Nonnegativity and positiveness of solutions to mass action reaction–diffusion systems

Original Paper


We show that solutions of a mass action chemical kinetics reaction–diffusion system are nonnegative. Conditions for components of the solution to be strictly positive or identically zero are given, based on an indexing procedure due to A. I. Volpert [Mat. Sb. (Russian) 88, 578–588 (1972); Math. USSR Sb. (English) 17, 571–582]. The results are illustrated with some examples.


Reaction-diffusion systems Chemical kinetics Positiveness 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.Department of ChemistryUniversity of LethbridgeLethbridgeCanada
  3. 3.Department of MathematicsUniversity of Wisconsin-MadisonMadisonUSA

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