TRAVELING WAVES IN A REACTION-DIFFUSION SYSTEM DESCRIBING SMOLDERING COMBUSTION.

Combustion is a fast oxidation process and exhibits diverse behaviors according to experimental conditions. When there is no natural convection of air, such as in experiments aboard a space shuttle or in a vertically confined system, an unexpected finger-like smoldering combustion develops. In this paper, a reaction-diffusion-advection system that describes smoldering combustion is studied from the viewpoint of computer-aided analysis. In particular, we focus on the traveling wave solutions of the system, which represent the characteristic propagation of combustion. It is revealed that the existence or nonexistence of stable traveling wave solutions determines whether or not a combustion front propagates in a self-sustained way in one space dimension. In two space dimensions, we numerically suggest the existence of a traveling spot solution in which the flow rate is too low to support planar traveling wave solutions. Moreover, we discuss reflection phenomena of a combustion wave when it reaches the boundary of the system. [ABSTRACT FROM AUTHOR]