The propagation of a flame front with a p- Laplacian operator

Abstract

The goal of the presented study is to provide a mathematical analysis for modeling a flame propagation dynamics with a p-Laplacian oper- ator. We extend some results already contemplated in the literature. Given the introduction of a new nonlinear operator, we first discuss the regularity and boundedness of solutions. Afterward, we obtain results concerning the existence and uniqueness of solutions. The second part of the paper is focused on the exploration of stationary and nonstationary solutions. The stationary solutions are constructed based on the definition of a Hamiltonian and a perturbation proce- dure. The non-stationary solutions are obtained with a single-point exponential scaling that ends in a Hamilton-Jacobi equation. This last equation is solved based on an asymptotic separation of variables technique