This paper presents a new nonlinear reaction–diffusion–convection system coupled with a system of ordinary differential equations that models a combustion front in a multilayer porous medium. The model includes heat transfer between the layers and heat loss to the external environment. A few assumptions are made to simplify the model, such as incompressibility; then, the unknowns are determined to be the temperature and fuel concentration in each layer. When the fuel concentration in each layer is a known function, we prove the existence and uniqueness of a classical solution for the initial and boundary value problem for the corresponding system. The proof uses a new approach for combustion problems in porous media. We construct monotone iterations of upper and lower solutions and prove that these iterations converge to a unique solution for the problem, first locally and then, in time, globally.

本文提出了一种新的非线性反应-扩散-对流系统，该系统与一个常微分方程组结合，可对多层多孔介质中的燃烧前沿进行建模。该模型包括各层之间的热传递以及向外部环境的热损失。为了简化模型，做了一些假设，例如不可压缩性。然后，将未知数确定为每一层中的温度和燃料浓度。当每一层中的燃料浓度是已知函数时，我们证明了相应系统的初始值和边值问题的经典解的存在性和唯一性。该证明使用了一种新方法来解决多孔介质中的燃烧问题。