Analysis and profiles of solution for a highly nonlinear model of pressure driven flame propagation in nonhomogeneous medium

Abstract

Purpose: This article aims to study a model of flame propagation in a nonhomogeneous medium with a p-Laplacian operator. The intention with such operator is to model the effects of slow and fast diffusion, that can appear in a nonhomogeneous media, depending on the pressure driven conditions. In addition, the authors introduce a general form in the reaction term, that introduces the flame chemical kinetics.

Design/methodology/approach: To introduce the governing equations, the authors depart from previously reported models in flame propagation, but the authors consider a new modeling approach based on a p-Laplacian operator.

Findings: The authors provide evidences of regularity and uniqueness of solutions. Afterward, the authors introduce profiles of stationary solutions based on the definition of a Hamiltonian for the newly discussed model. Eventually, the authors obtain exponential profiles solutions with the help of a scaling, that transforms the model into a nonlinear Hamilton–Jacobi equation.

Originality/value: The new model has not been previously reported in the literature. The authors consider that the mathematical properties of a p-laplacian (in particular the property known as finite propagation) is of inherent interest to model pressure drive flames with slow or fast diffusion. Indeed, the authors’ approach has the value of providing an operator that can fit better to model flame propagation. In addition, the authors introduce a general form of chemical kinetics, to make the authors’ model further general.