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Dissertation Defense: Elena Gurvich

semigroup methods in multi-physics poroelasticity


Mathematics/Psychology : 412

Date & Time

May 24, 2024, 11:00 am1:30 pm


Title: Semigroup Methods for Poroelastic Multi-Physics Systems Describing Biological Tissues

Abstract: The mathematical theory of poroelasticity was developed for geoscience applications (e.g., petroleum engineering). More recently, it has been incorporated into biological and biomedical engineering models (e.g., artificial organs, arterial stents, scaffolding), owing to the poroelastic nature of biological tissues. Poroelastic systems, typically described by Biot's equations, relate saturated porous structural deformations to fluid pressure changes, are. For the parameters of physical interest, a quasi-static approximation leads to dynamics which can be represented as an implicit evolution. Moreover, compressibility in Biot's equations is a significant consideration, in the incompressible limit, Biot's model degenerates.

We will present a biologically-motivated multilayered system. The coupled dynamics of a 3D poroelastic structure, a poroelastic plate, and an incompressible free Stokes flow. We propose two constituent sub-problems, to gain a better understanding of this extremely complex system. First, a complete well-posedness analysis of the poroelastic plate is shown utilizing variational tools. Secondly, a Biot-Stokes filtration problem is proposed with Beavers-Joseph-Saffman coupling conditions on a fixed 2D interface. A semigroup approach is used to bypass the issues with mismatched trace regularities on the interface; thus guarantee strong and generalized solutions. Then an argument by density is shown to yield weak solutions, including the degenerate case where. The most interesting cases are singular limits, leading us to use abstract implicit, degenerate evolutions, of which we provide a brief overview. Thus, we provide a clear elucidation of strong solutions and a construction of weak solutions for both poroelastic plate and inertial linear Biot-Stokes filtration systems, as well as their regularity through associated estimates.

Bedrich Sousedik, UMBC
Rouben Rostamian, UMBC
Andrei Draganescu, UMBC
Animikh Biswas, UMBC, Reader
George Avalos, University of Nebraska-Lincoln, Reader
Justin Webster, UMBC, Chair

Virtual Information: 

Ellie Gurvich Ph.D. Defense
Friday, May 24 · 11:00am – 1:00pm
Time zone: America/New_York
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