International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 10, Pages 581-607
doi:10.1155/S0161171201006706
A mathematical analysis of thermal explosions
Institute of Mathematics, University of Tsukuba, Tsukuba 305-8571, Japan
Received 16 February 2001
Copyright © 2001 Kazuaki Taira. 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.
Abstract
This paper is devoted to the study of semilinear degenerate elliptic boundary value problems arising in
combustion theory which obey the simple Arrhenius rate law and a
general Newton law of heat exchange. We prove that ignition and
extinction phenomena occur in the stable steady temperature
profile at some critical values of a dimensionless rate of heat
production.