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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.
Bibliography Note
Includes bibliographical references.
Advisory Committee
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.
Publisher
Florida State University
Identifier
FSU_migr_etd-2182
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