Analysis of travelling waves and propagating supports for a nonlinear model of flame propagation with a p-Laplacian operator and advection

In this paper, we propose a new model to characterize the behaviour of a flame driven by temperature and pressure variables. The model is formulated using a p-Laplacian operator, an advection term, and a nonlinear reaction (considering linear kinetics). First, the uniqueness and boundedness of the weak solutions are demonstrated. Subsequently, traveling wave solutions supported by the geometric perturbation theory are obtained. As a major outcome, minimum traveling wave speeds are shown to exist, for which the associated profiles of the solutions are purely monotonic with exponential behaviour. The assumptions considered in the analytical approach are further explored through a numerical assessment, and self-similar solutions are constructed to determine the evolution of the flame front in terms of the temperature and pressure variables.