Modeling wildfire dynamics through a physics-based approach incorporating fuel moisture and landscape heterogeneity

The paper presents a consistent ADR wildfire model with Rosseland (T^3) diffusion, a step ignition law, and moisture via apparent heat capacity, and reports qualitative/numerical findings: ROS decreases with moisture (stopping at high M when w=0), increases with wind, nonzero ROS for any nonzero wind, and practical equivalence of Arrhenius vs constant reaction rate after calibration. However, it does not provide rigorous traveling-wave existence or monotonicity proofs. The candidate solution sketches such proofs and gives plausible arguments (Kirchhoff transform, maximum principle bounds, an energy identity, monotone iteration, and qualitative Melnikov-type comparisons), but key steps are only outlined and require missing hypotheses (e.g., precise Fredholm/transversality conditions, full control of the discontinuous ignition limit, and a justified nonnegative remainder in the projected identity). Hence, the paper is correct but not a proof paper; the model solution is promising but incomplete.