On the Travelling Wave Solutions of a Non-linear Reaction-Diffusion-Advection Model for Forest Fire Spread

This preliminary work investigates the dynamics of forest fire propagation using an Advection-Diffusion-Reaction (ADR) model with a non-linear diffusion term. A central focus of this work is the study of specific conditions under which travelling wave solutions occur within the ADR considered model, extending existing literature to a more general, one-dimensional (1D), non-linear diffusion case. The model approximation is validated through numerical simulations, demonstrating its effectiveness in capturing the front dynamics of wildfire propagation. The results confirm the model’s reliability in identifying the critical wave speed of propagation, for the studied cases, offering a potential valuable tool for risk mitigation and strategic territorial planning.