Continuous dependence on boundary and Soret coefficients in double diffusive bidispersive convection

Abstract

We develop a theory for double diffusive convection in a double porosity material along the Brinkman scheme. The Soret effect is included whereby a temperature gradient may directly influence salt concentration. The boundary conditions on the temperature and salt fields are of general Robin type. A number of a priori estimates are established whereby, through energy arguments, we prove continuous dependence of the solution on the Soret coefficient and on the coefficients in the boundary conditions in the L2‐ norm.