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Structural stability for the Brinkman equations of porous media. (English) Zbl 0859.76065

Summary: Explicit a priori continuous dependence estimates are derived for the Brinkman equations for non-isothermal flow in porous media. Continuous dependence on the cooling coefficient is shown when a boundary condition of Newton cooling type is employed. Continuous dependence on the model itself is proved when the Boussinesq model is allowed to change to one appropriate to penetrative convection. The final result derives an a priori continuous dependence estimate for the heat supply and body force.

MSC:

76S05 Flows in porous media; filtration; seepage
35B35 Stability in context of PDEs
35Q35 PDEs in connection with fluid mechanics
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