Abstract
The structural stability of a double diffusive convection in a porous medium of the
Forchheimer type was studied, when the density of fluid depends on temperature and
concentration as a cubic and linear function, respectively. It has been shown that for this problem,
with thermal convection in a plane infinite layer, the resonance can occur between the internal
layers that arise. The main parameter is the internal heat source and its presence may lead to
oscillatory convection in linear instability inducing resonance. Thus, in this study, the structural
stability problem of continuous dependence on the heat source itself for a model of nonisothermal
flow in a porous medium of Forchheimer type was analyzed. Furthermore, the continuous
dependence of the solution on changes in the Forchheimer coefficients has been shown.
Forchheimer type was studied, when the density of fluid depends on temperature and
concentration as a cubic and linear function, respectively. It has been shown that for this problem,
with thermal convection in a plane infinite layer, the resonance can occur between the internal
layers that arise. The main parameter is the internal heat source and its presence may lead to
oscillatory convection in linear instability inducing resonance. Thus, in this study, the structural
stability problem of continuous dependence on the heat source itself for a model of nonisothermal
flow in a porous medium of Forchheimer type was analyzed. Furthermore, the continuous
dependence of the solution on changes in the Forchheimer coefficients has been shown.
Keywords
Cubic density.
Darcy’s law
Double diffusive
Forchheimer theory
structural stability