Classical solution for a nonlinear hybrid system modeling combustion in a multilayer porous medium. (February 2022)

• Record Type: Journal Article
• Authors: Batista, M.R.; Da Mota, J.C.; Santos, R.A.
• Is Part Of: Nonlinear analysis. Volume 63(2022)
• Publication Date: 2022-02
• Subjects: Reaction–diffusion–convection system -- Combustion -- Multilayer porous medium -- Schauder's fixed-point -- Zorn's lemma -- Maximal solution; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103406
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: Combustion processes in porous media have been used by the petroleum engineering industry to extract heavy oil from reservoirs. This study focuses on a one-dimensional nonlinear hybrid system consisting of n reaction–diffusion–convection equations coupled with n ordinary differential equations, which models a combustion front moving through a porous medium with n parallel layers. The state variables are the temperature and fuel concentration in each layer. Coupling occurs in both the reaction function and differential operator coefficients. We prove the existence of a classical solution, first locally and then globally over time, to an initial and boundary value problem for the corresponding system. The proof uses a new approach for combustion problems in porous media. The local solution is obtained by defining an operator in a set of Hölder continuous functions and using Schauder's fixed-point theorem to find a fixed point as the desired solution. Using Zorn's lemma, we extend the local solution to a global solution, proving that the first-order spatial derivative of the temperature in each layer is a bounded function.