Citation

Derrick WR, Kalachev LV, Cima JA. Math. Comput. Model. 2007; 46(5-6): 612-624.

Copyright

(Copyright © 2007, Elsevier Publishing)

DOI

10.1016/j.mcm.2006.11.030

PMID

unavailable

Abstract

In certain combustion models, an initial temperature profile will develop into a combustion wave that will travel at a specific wave speed. Other initial profiles do not develop into such waves, but die out to the ambient temperature. There exists a clear demarcation between those initial conditions that evolve into combustion waves and those that do not. This is sometimes called a watershed initial condition. In this paper we will show that there may be numerous exact watershed conditions to the initial-Neumann-boundary value problem, with ux(0,t)=ux(1,t)=0, on I=[0,1]. They are composed from the positive non-constant solutions of , with vx(0)=vx(1)=0, for small values of D. We will give easily verifiable conditions for when combustion waves arise and when they do not.