Application of the semigroup theory to a combustion problem in a multi-layer porous medium (original) (raw)

This study proved that the Cauchy problem for a one-dimensional reaction-diffusion-convection system is locally and globally well-posed in H 2 (R). The system modeled a gasless combustion front through a multi-layer porous medium when the fuel concentration in each layer was a known function. Combustion has critical practical porous media applications, such as in in-situ combustion processes in oil reservoirs and several other areas. Earlier studies considered physical parameters (e.g., porosity, thermal conductivity, heat capacity, and initial fuel concentration) constant. Here, we consider a more realistic model where these parameters are functions of the spatial variable rather than constants. Furthermore, in previous studies, we did not consider the continuity of the