Backward-Propagating Combustion Waves in a Reaction-Diffusion-Convection System

In this study, we analyze combustion waves in a simplified one-dimensional model for porous media, focusing on the case of backward propagating combustion where the combustion front moves opposite to the direction of the injected airflow, resulting in negative wave velocity. The mathematical model consists of three coupled partial differential equations governing temperature, oxygen, and fuel concentrations. Assuming that oxygen is transported faster than heat, we reduce the system to a form suitable for phase plane analysis and establish the existence of counterflow traveling wave solutions. Our work extends previous results on coflow combustion waves by providing a comprehensive classification of counterflow wave types and their properties. The existence and structure of these waves are rigorously demonstrated through dynamical systems techniques, offering new insights into the behavior of combustion fronts in porous media.