Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 23, pp. 1-18.

Title: Local solutions for a Brinkman equation coupled with heat-convective and concentration-diffusive equations and a volumetric mass source

Author: Hakho Hong (State Academy of Sciences, Pyongyang, DPR Korea)
  
Abstract:
In this article, we consider a model coupled with the Brinkman 
heat-convective and concentration-diffusive equations for a mixed gas 
flow in a porous media. The specificity of this model lies in the 
presence of a volumetric mass source depending on  temperature and 
concentration in mass balance equation. We will prove the 
existence and uniqueness of the smooth local solutions for the 
3-D Cauchy problem. As a byproduct, we show the convergence of  the 
approximate solutions based on an iteration scheme.

Submitted September 30, 2024. Published March 03, 2025.
Math Subject Classifications: 35B40, 35B65, 35L65, 76N05, 76N10, 76T10.
Key Words: Brinkman equation; heat-convective equation; mixed model;
  concentration-diffusive equation; existence; uniqueness; iteration scheme.