Finger-like smoldering patterns are observed in experiments under microgravity. For theoretical understanding of such pattern phenomena, a model of reaction-diffusion system has been proposed. In this paper, we prove the existence and uniqueness of a solution for this reaction-diffusion system. We also consider a large-time behavior of solutions.
"Mathematical treatment of a model for smoldering combustion." Hiroshima Math. J. 38 (3) 349 - 361, November 2008. https://doi.org/10.32917/hmj/1233152774