Fluid flows through deformable porous media are relevant for many applications in biology, medicine and bio-engineering, including tissue perfusion and fluid flow inside cartilages and bones. We are interested in perfusion inside the eye and its connection to the development of glaucoma. Mathematically, the problem translates into the study of a quasi-static nonlinear poroelastic system, which is a system of PDEs of mixed parabolic-elliptic type. We answer questions related to ocular tissue biomechanics via well-posedness, sensitivity analysis, and optimal control for the PDE coupled system applied to the eye.
Poroelastic Systems: Analysis, Sensitivity, and Control
Lorena Bociu, NC State University
2022 AWM Research Symposium
Systems and Control