Global well-posedness for a quasilinear combustion model in multilayer porous media

Abstract

We investigate a class of nonlinear reaction-diffusion-convection systems modeling combustion fronts in multilayer porous media. The model describes the coupled dynamics of temperature and fuel concentration, departing from previous approaches that assumed prescribed fuel profiles to simplify the analysis. By integrating the fuel concentration equations, we derive a non-autonomous quasilinear evolution problem formulated purely in terms of the temperature vector. To address the analytical difficulties arising from the absence of a linear part in the differential operator, we introduce a higher-order regularization strategy that ensures control over second derivatives in Sobolev spaces. Using Banach’s fixed-point theorem and detailed Sobolev estimates, we establish global-in-time existence, uniqueness, and continuous dependence on both initial data and model parameters. By removing the assumption of prescribed fuel profiles and regularizing the fully nonlinear system, this work provides the first global well-posedness result for a quasilinear combustion model in multilayer porous media, with numerical simulations confirming the theoretical predictions and capturing physically consistent front propagation.