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Continuous dependence on boundary and Soret coefficients in double diffusive bidispersive convection
Author(s) -
Franchi Franca,
Nibbi Roberta,
Straughan Brian
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6581
Subject(s) - double diffusive convection , mathematics , thermophoresis , convection , boundary (topology) , a priori and a posteriori , boundary value problem , norm (philosophy) , mathematical analysis , porous medium , thermodynamics , porosity , natural convection , thermal , chemistry , physics , rayleigh number , nanofluid , philosophy , organic chemistry , epistemology , political science , law
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 L 2 ‐ norm.