Original Paper

Journal of Mathematical Chemistry

, Volume 42, Issue 4, pp 1135-1145

First online:

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

  • Maya MinchevaAffiliated withDepartment of Applied Mathematics, University of WaterlooDepartment of Chemistry, University of LethbridgeDepartment of Mathematics, University of Wisconsin-Madison Email author 
  • , David SiegelAffiliated withDepartment of Applied Mathematics, University of Waterloo

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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