Abstract
In the Darcy–Boussinesq–Brinkman scheme, the onset of convection in a porous horizontal layer \(\mathtt L \) with depth-dependent permeability and viscosities is investigated. The linear instability is studied and the global nonlinear stability is investigated via the auxiliary system method. By looking for symmetries and skew-symmetries hidden in the Darcy–Boussinesq–Brinkman model, a condition, in closed form, guaranteeing the global nonlinear stability is furnished. Applications to the earth’s mantle and to artificial porous materials are furnished.
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