## Applied Mathematics Colloquium: Dr. Boris Muha

#### University of Zagreb

**Title:**Modeling and Analysis of Fluid-Structure Interactions Arising in Hemodynamics

**Speaker: **Boris Muha, University of Zagreb

**Abstract:**Fluid-structure interaction (FSI) problems describe the dynamics of multi-physics systems that involve fluid and solid components. These are everyday phenomena in nature, and arise in various applications ranging from biomedicine to engineering. Mathematically, FSI problems are typically non-linear systems of partial differential equations (PDEs) of mixed hyperbolic-parabolic type, defined on time-changing domains (i.e., moving boundaries).

In this talk I will formulate an FSI problem describing blood through a compliant vessel treated with biomedical device called a stent. I will illustrate the main features of the FSI problem, as well as main challenges arising in the PDE analysis of such FSI problems. I will also describe a numerical method for a class of FSI problems that, in this case, leads to a proof of existence of weak solutions to the PDE system.