ANALYSING THE EXISTENCE AND UNIQUENESS SOLUTION OF A WILDFIRE MODEL WITH DIFFUSION AND CONVECTION OF MOISTURE

Abstract

Wildfire spread modeling is governed by a complex system of non-linear partial differential equations (PDEs) that capture the intricate dynamics of wildfire behavior, including heat transfer and moisture interaction. A comprehensive understanding of these dynamics is critical for developing effective management, mitigation, and intervention strategies. In this study, temperature-dependent diffusion and convection terms are incorporated into the volume fraction of moisture, enriching the model framework and improving its accuracy in representing wildfire spread. To ensure the mathematical robustness of the model, the non-linear PDE system is transformed into a dimensionless form using appropriate dimensionless variables, facilitating the analysis of the equations. The model equations describe the dynamics of combustible forest material (CFM) in terms of the volume fractions of dry organic matter, moisture, coke, heat, and oxygen. The conditions for the existence and uniqueness of solutions to the model equations are rigorously established using the Lipschitz continuity criterion. The results confirm that unique solutions exist when the Lipschitz conditions are satisfied.