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

Al-Refai, Mohammed; Katatbeh, Qutaibeh

doi:https://doi.org/10.1155/IJMMS/2006/24391

International Journal of Mathematics and Mathematical Sciences

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Volume 2006 | Article ID 024391 | https://doi.org/10.1155/IJMMS/2006/24391

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

Mohammed Al-Refai¹and Qutaibeh Katatbeh¹

Received07 Dec 2005

Revised31 May 2006

Accepted05 Jun 2006

Published14 Sept 2006

Abstract

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.

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Copyright

Copyright © 2006 Hindawi Publishing Corporation. 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.

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