Global existence, traveling wave solutions and Hopf bifurcation analysis in a flame propagation model with nonlinear diffusion and advection

Abstract

This paper investigates the mathematical modeling of flame propagation in porous media through a system of partial differential equations incorporating nonlinear diffusion and advection terms. We propose an extended model based on previous studies, incorporating a bistable nonlinearity and examining its behavior under various conditions. The focus is on the existence, uniqueness, and global stability of traveling wave solutions, as well as a detailed Hopf bifurcation analysis to determine the stability of equilibrium points. Using Geometric Perturbation Theory, we analyze the system’s dynamics and derive conditions for the regular convergence of traveling wave solutions.