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
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.