  I examine some analytical properties of a nonlinear reaction-diffusion system
that has been used to model the propagation of a wildfire. I establish
global-in-time existence and uniqueness of bounded mild solutions to the Cauchy
problem for this system given bounded initial data. In particular, this shows
that the model does not allow for thermal blow-up. If the initial temperature
and fuel density also satisfy certain integrability conditions, the $L^2$-norms
of these global solutions are uniformly bounded in time. Additionally, I use a
bootstrap argument to show that small initial temperatures give rise to
solutions that decay to zero as time goes to infinity, proving the existence of
initial states that do not develop into travelling combustion waves.
