Solutions for a flame propagation model in porous media based on Hamiltonian and regular perturbation methods

This article extends the exploration of solutions to the issue of flame propagation driven by pressure and temperature in porous media that we introduced in earlier papers. We continue to consider a p-Laplacian type operator as a mathematical formalism to model slow and fast diffusion effects, that can be given in the non-homogeneous propagation of flames. In addition, we introduce a forced convection to model any possible induced flow in the porous media. We depart from previously known models to further substantiate our driving equations. From a mathematical standpoint, our goal is to deepen in the understanding of the general behavior of solutions via analyzing their regularity, boundedness, and uniqueness. We explore stationary solutions through a Hamiltonian approach and employ a regular perturbation method. Subsequently, nonstationary solutions are derived using a singular exponential scaling and, once more, a regular perturbation approach.