In this paper we present a global existence and uniqueness result of solutions to a system consisting of a coupled nonlinear PDE and a nonlinear ODE. This system is a one-dimensional fluiddynamic model for tunnel fires and was presented in I. Gasser and J. Struckmeier and then analyzed in I. Gasser and in I. Gasser and H. Steinrück with respect to the applications
"On the existence of transient solutions of a tunnel fire model." Commun. Math. Sci. 4 (3) 609 - 619, September 2006.