Graduate Studies

 

First Advisor

George Avalos

Degree Name

Doctor of Philosophy (Ph.D.)

Department

Mathematics

Date of this Version

8-2024

Document Type

Dissertation

Citation

A dissertation presented to the faculty of the Graduate College of the University of Nebraska in partial fulfillment of requirements for the degree of Doctor of Philosophy

Major: Mathmatics

Under the supervision of Professor George Avalos

Lincoln, Nebraska, August 2024

Comments

Copyright 2024, Sara McKnight. Used by permission

Abstract

The coupling of a porous medium modeled by the Biot equations and a fluid has many biological applications. There are numerous ways by which to model the fluid and to couple the porous medium with the fluid. This particular model couples the Biot equations to Stokes flow along the boundary, through the Beavers-Joseph-Saffman conditions. We address semigroup well-posedness of the system via an inf-sup approach, which along the way requires consideration of a related but uncoupled static Biot system. We also present the results of finite element analysis on both the uncoupled Biot system and the coupled system.

Advisor: Sara McKnight

Included in

Mathematics Commons

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