Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

Committee Member

Dr. Vincent Ervin, Committee Chair

Committee Member

Dr. Timo Heister

Committee Member

Dr. Lea Jenkins

Committee Member

Dr. Hyesuk Lee


This thesis investigates two nonlinear systems of time-dependent partial differential equations that model a filtration process. Existence and uniqueness results for the governing equations is established. For each system, a finite element scheme capable of approximating the solutions is investigated. Accompanying numerical experiments corroborate the analytical findings. Finally, an optimization application concerning the design of a filter is discussed and supported with a numerical study.



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