Journal of Applied Mathematics and Decision Sciences
Volume 4 (2000), Issue 2, Pages 151-163

Comparison theorems for multicomponent diffusion systems: developments since 1961

M. I. Nelson

Department of Fuel and Energy, The University of Leeds, Leeds LS2 9JT, UK

Copyright © 2000 M. I. Nelson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Comparison theorems may be used to prove the existence and uniqueness of solutions to certain types of partial differential equations. They provide bounds for solutions and can be used as the basis of numerical techniques for the computation of solutions. In 1961 Alex McNabb published one of the first papers extending their use to multi-component systems. Developments in the theory and applications of such results, through citations of this original paper, are reviewed.