Continuous Dependence on the Heat Source in Resonant Porous Penetrative Convection
Brian Straughan · Studies in Applied Mathematics · 2011
I study the structural stability for a problem in a porous medium when the density of saturating liquid is a nonlinear function of temperature and an internal heat source is present. It has been shown that for this problem when one considers thermal convection in a plane infinite layer then resonance may occur between internal layers that arise. A key parameter is the internal heat source and its presence may lead to oscillatory instability inducing resonance. Therefore, in this paper, I analyze the general structural stability problem of continuous dependence on the heat source itself for a model of nonisothermal flow in a porous medium of Forchheimer type, in a general three‐dimensional domain.