Lorena Bociu
NC State University, Raleigh, USA

We present new results related to well-posedness, sensitivity analysis, and optimal control problems for quasi-static nonlinear poroelastic systems with applications in biomechanics. The PDE systems under consideration represent nonlinear, implicit, degenerate evolution problems, which fall outside of the well-known implicit semigroup monotone theory. We also consider scenarios where the local, accurate, 3D poroelastic PDE systems are coupled with systemic, 0D, lumped models of the remainder of blood circulation, in order to account for the global features of the problem. Our results have applications in biology, medicine and bio-engineering, including tissue perfusion, fluid flow inside cartilages and bones, and design of bioartificial organs.