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

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.