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This dissertation investigates asymptotic behaviour of convection in a fluid saturated porous medium. We analyse the Darcy-Boussinesq system under perturbation of the Darcy-Prandtl number parameter. In very tightly packed media this parameter is of very large order and can be driven to infinity to yield the infinite Darcy-Prandtl number model. We show convergence of global attractors and invariant measures of the Darcy-Boussinesq system to that of the infinite Darcy-Prandtl number model with respect to perturbation of the Darcy-Prandtl number parameter.
A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Includes bibliographical references.
Xiaoming Wang, Professor Directing Dissertation; Ming Ye, Outside Committee Member; Bettye Anne Case, Committee Member; Brian Ewald, Committee Member; Alec N.Kercheval, Committee Member; Craig Nolder, Committee Member.
Florida State University
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