@article{ref1,
title="Collapsing heat waves",
journal="Mathematical and computer modelling",
year="2007",
author="Derrick, William R. and Kalachev, Leonid V. and Cima, Joseph A.",
volume="46",
number="5-6",
pages="612-624",
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.<p />",
language="",
issn="0895-7177",
doi="10.1016/j.mcm.2006.11.030",
url="http://dx.doi.org/10.1016/j.mcm.2006.11.030"
}