International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 24391, 13 pages

Upper and lower bounds for a reactive-diffuse system with Arrhenius kinetics

Mohammed Al-Refai and Qutaibeh Katatbeh

Department of Mathematics and Statistics, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan

Received 7 December 2005; Revised 31 May 2006; Accepted 5 June 2006

Copyright © 2006 Mohammed Al-Refai and Qutaibeh Katatbeh. 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 arguments are used to study a problem in combustion theory consisting of a nonlinear parabolic equation together with initial and boundary conditions. Upper and lower bounds for the problem are constructed. The lower solutions are used to determine whether the solution of the problem is increasing in time for certain initial condition. Numerical results are presented for the slab, infinite cylinder, and unit sphere. The bounds are compared with the existing ones in the literature for the slab geometry.