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This book investigates asymptotic behaviour of convection in a fluid saturated porous medium. We analyse the DarcyBoussinesq system under perturbation of the DarcyPrandtl number parameter. In very tightly packed media this parameter is of very large order and can be driven to innity to yield the innite DarcyPrandtl number model. We show convergence of global attractors and invariant measures of the DarcyBoussinesq system to that of the innite DarcyPrandtl number model with respect to perturbation of the Darcy Prandtl number.
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