DE Seminar: Galen Richard (UMBC)

The filtration system considered here consists of 3D Stokes flow, coupled to a multilayered poroelastic structure of recent interest. This structure comprises a "2.5" dimensional linear poroelastic plate system at the boundary of bulk (3D) poroelastic system. The motivating scenario for this model is blood flow around and through biological tissue (arterial dynamics and organ systems). 

Recent work has demonstrated the existence of weak solutions for this system using time discretization and energy methods, but uniqueness and regularity remained open. The central challenges involve the multiphysics coupling, the nonstandard weak formulation for physical coupling conditions, and low regularity of hyperbolic dynamics at the interface. Our goal in this talk is to utilize a semigroup approach to prove existence, uniqueness, and robustness of strong and mild solutions for the dynamics. This approach circumvents the traceregularity mismatches, and is amenable to future numerical work and stability analysis.
A fluid-pressure sub-problem is formulated to eliminate the fluid-pressure from the state space, and a mixed-variational (Babuska-Brezzi) system is constructed in the frequency domain to achieve maximality of the dynamics operator.