Spatial decay estimates for the Brinkman and Darcy flows in a semi-infinite cylinder

Effect of anisotropic permeability on Darcy's law

“…Payne [30][31][32] is a series of papers which study continuous dependence on geometry and on the model: many papers followed after these. Payne and Song [6] and Qin and Kaloni [12] study spatial decay of solutions to porous media models of Darcy, Brinkman, and Brinkman-Forchheimer type. Payne et al [7] analyses the equations for convective uid motion in a porous medium of Brinkman or Forchheimer type but when the viscosity varies with either temperature or salt concentration: important practical situations such as salinization in soil [33] require models which incorporate strong viscosity variation.…”

“…Indeed, the books of Ames and Straughan [1], Bellomo and Preziosi [2] and Flavin and Rionero [3], see also Doering and Gibbon [4], include detailed accounts of structural stability. Continuous dependence on the model itself in studies of ows in porous media is very much the focus of attention in the recent papers of Franchi and Straughan [5], Payne and Song [6], Payne et al [7], Payne and Straughan [8][9][10][11], Qin and Kaloni [12] and Straughan and Hutter [13]. When we refer to the equations for ow in porous media we have in mind the well accepted equations of Darcy [14] and their ramiÿcations, cf.…”

Spatial Decay Estimates in Time-Dependent Double-Diffusive Darcy Plane Flow

“…More recent work on decay results in porous medium problems has been carried out by Payne and Song [11,12], Chadam and Qin [2], and Qin and Kaloni [13].…”

Spatial decay bounds for double diffusive convection in Brinkman flow

“…With prescribed data on the finite end of the cylinder together with appropriate homogeneous initial conditions and boundary conditions on the lateral surface, Saint-Venant type decay results are established. Other decay results for porous medium problems have been obtained by Payne and Song [9], and Song [11]. For a survey of results of Saint-Venant type see Horgan and Knowles [5], Horgan [3,4].…”