Journal of Mathematical Chemistry

, Volume 42, Issue 4, pp 1135–1145

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


    • Department of Applied MathematicsUniversity of Waterloo
    • Department of ChemistryUniversity of Lethbridge
    • Department of MathematicsUniversity of Wisconsin-Madison
  • David Siegel
    • Department of Applied MathematicsUniversity of Waterloo
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 systemsChemical kineticsPositiveness

Copyright information

© Springer Science+Business Media, LLC 2007