Asymptotics of the solution of a system of singularly perturbed differential equations in the forest fire spread models

Abstract

We propose a forest fire model consisting of two equations, namely those describing the motion of the temperature front and the burned biomass front. To obtain a physically meaningful description of the solution behavior, we use equations with modular nonlinearity. For the proposed models, using asymptotic analysis methods, we have studied the existence of a solution in the form of a front. The asymptotic analysis allows us to estimate the speed of the front and determine the limits of the model applicability. When generalized to the two-dimensional case, the model can be used to simulate the motion of the combustion front in real forest fires, as well as to pose inverse problems for determining the amount of burned biomass after the passage of the combustion front.