Geometria finsler e incêndios florestais.

Abstract

The simplest analytical approach to model the propagation of wildfires considers that the velocity space is represented by an indicatrix at each point. Since then, elliptic modeling has been widely accepted. In A general model for wildfire propagtion with wind and slope, Javaloyes (2023) presents a more sophisticated model for fire propagation, taking into account the slope of the terrain and the contribution of wind, where the ellipse now coincides with the indicatrix of a Finsler metric. Finally, the behavior of the fire is modeled by a system of ODEs, or alternatively, the application of fire is also characterized by a system of PDEs with certain orthogonality conditions.