Journal of Mathematical Chemistry

, Volume 42, Issue 4, pp 1135–1145

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

Original Paper

DOI: 10.1007/s10910-007-9292-0

Cite this article as:
Mincheva, M. & Siegel, D. J Math Chem (2007) 42: 1135. doi:10.1007/s10910-007-9292-0


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 

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

Personalised recommendations