International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 10, Pages 581-607

A mathematical analysis of thermal explosions

Kazuaki Taira

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.


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.