The process of combustion is highly complex, because it usually involves turbulent mixing, heat transfer, radiation and chemistry. The fact that the combustion involves very different processes makes it not only a highly multidisciplinary topic for research, but also a highly challenging one. The aim of this work is to prove, based on the Faedo-Galerkin method, the existence of solutions for the Eulerian flamelet model equations and to obtain numerical results, via Large-Eddy Simulation (LES), for a piloted jet diffusion flame. The proof of the existence of solutions follow the Faedo-Galerkin method, which is frequently employed to proof the existence of solutions for evolution equations. For the simulation of combustion flows the LES technique seem to be good alternative, because combustion flows involve a large range of time and length scales that are originated from the heat release due to chemical reactions, which induce strong convective, diffusive and radiative heat transfer. The governing equations were integrated using the explicit Runge-Kutta multistage scheme and numerical tests were carried out for Sandia Flame D. The results are in agreement with datafound in the literature.