| Abstract: |
| Modeling of fluid flows through porous deformable media is relevant for many applications in biology, medicine and bioengineering, like tissue perfusion and fluid flow inside cartilages and bones. These fluid-structure mixtures are described by nonlinear poro-visco-elastic systems on bounded domains. The boundary conditions are the primary drivers of the dynamics of these systems. Their influence over and ability to control the solution is an important open question, with beneficial implications in the development of novel strategies to improve experimental and clinical approaches in bio-engineering and medicine. In this talk we focus on (i) well-posedness and regularity of solution, (ii) the role of structural viscoelasticity, and (iii) sensitivity analysis as precursor for optimization and control problems for these porous media flows. Lastly, we discuss applications of our results in the case of perfusion of the optic nerve head, and its connections to the development of glaucoma. |
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