We consider an elliptic-parabolic coupled partial differential equation connected to a nonlinear ODE through an interface. The model describes fluid flowing through biological tissues with the ODE accounting for global features of blood flow that affect the tissue. We discuss a modeling choice on the interface coming from the fact that the ODE is 0D and the PDE is 3D and show existence of a solution to this problem using semigroup theory for implicit evolution and a contraction mapping.
Existence Theory of Multi-Scale Interface Coupling between Deformable Porous Media and Lumped Hydraulic Circuits
Sarah Strikwerda, University of PennsylvaniaAuthors: Lorena Bociu, Matthew Broussard, Giovanna Guidoboni
2023 AWM Research Symposium
Recent Developments in Control, Optimization, and the Analysis of Partial Differential Equations [Organized by Lorena Bociu and Pelin Guven Geredeli]