Page 500 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 500
MATHEMATICAL ANALYSIS: THE INTERACTION OF FLUIDS/ VISCOELASTIC
MATERIALS AND SOLIDS (MS-36)
Qualitative Analysis of a Lamé-Wave-Stokes/Navier-Stokes System
George Avalos, gavalos2@unl.edu
University of Nebraska-Lincoln, United States
In this talk, we will discuss an appropriate Babuška-Brezzi variational formulation, and subse-
quent spectral and stability analysis for a multilayered structure-fluid interaction (FSI) which
arises in the mathematical modeling of vascular blood flow. The coupled PDE system which
we will consider mathematically accounts for the fact that mammalian veins and arteries will
typically be composed of various layers of tissues: each layer will generally manifest its own
intrinsic material properties, and will moreover be separated from the other layers by thin elas-
tic laminae. Consequently, the resulting modeling FSI system will manifest an additional PDE,
which evolves on the boundary interface, so as to account for the thin elastic layer. (This is in
contrast to the FSI PDE’s which appear in the literature, wherein elastic dynamics are largely
absent on the boundary interface.) As such,the PDE system will constitute a coupling of 3D
fluid-2D wave-3D elastic dynamics. This is joint work with Pelin Güven Geredeli.
Fluid-poroelastic structure interaction motivated by the design of a
bioartificial pancreas
Suncˇica Cˇ anic´, canics@berkeley.edu
University of California Berkeley, United States
In this talk we present a recent well-posedness result in the area of fluid-poroelastic struc-
ture interaction, motivated by the design of a first implantable bioartificial pancreas without
the need for immunosuppressant therapy. We show global existence of a weak solution to a
fluid-structure interaction (FSI) problem between the flow of an incompressible, viscous fluid,
modeled by the time-dependent Stokes equations, and a multi-layered poroelastic medium con-
sisting of a thin poroelastic plate and a thick poroelastic medium modeled by a Biot model. This
is the first global (weak) solution existence result in the context of poroelastic FSI. Numerical
simulations of the underlying problem showing optimal design of a bioartificial pancreas, will
be presented. If time permits, I will also preview a well-posedness results for a stochastically
perturbed FSI problem. This is a joint work with bioengineer Shuvo Roy (UCSF), and mathe-
maticians Yifan Wang (UCI), Lorena Bociu (NCSU), Boris Muha (University of Zagreb), and
Justin Webster (University of Maryland, Baltimore County). The stochastically perturbed FSI
result was obtained with PhD student Jeffrey Kuan (UC Berkeley).
498
MATERIALS AND SOLIDS (MS-36)
Qualitative Analysis of a Lamé-Wave-Stokes/Navier-Stokes System
George Avalos, gavalos2@unl.edu
University of Nebraska-Lincoln, United States
In this talk, we will discuss an appropriate Babuška-Brezzi variational formulation, and subse-
quent spectral and stability analysis for a multilayered structure-fluid interaction (FSI) which
arises in the mathematical modeling of vascular blood flow. The coupled PDE system which
we will consider mathematically accounts for the fact that mammalian veins and arteries will
typically be composed of various layers of tissues: each layer will generally manifest its own
intrinsic material properties, and will moreover be separated from the other layers by thin elas-
tic laminae. Consequently, the resulting modeling FSI system will manifest an additional PDE,
which evolves on the boundary interface, so as to account for the thin elastic layer. (This is in
contrast to the FSI PDE’s which appear in the literature, wherein elastic dynamics are largely
absent on the boundary interface.) As such,the PDE system will constitute a coupling of 3D
fluid-2D wave-3D elastic dynamics. This is joint work with Pelin Güven Geredeli.
Fluid-poroelastic structure interaction motivated by the design of a
bioartificial pancreas
Suncˇica Cˇ anic´, canics@berkeley.edu
University of California Berkeley, United States
In this talk we present a recent well-posedness result in the area of fluid-poroelastic struc-
ture interaction, motivated by the design of a first implantable bioartificial pancreas without
the need for immunosuppressant therapy. We show global existence of a weak solution to a
fluid-structure interaction (FSI) problem between the flow of an incompressible, viscous fluid,
modeled by the time-dependent Stokes equations, and a multi-layered poroelastic medium con-
sisting of a thin poroelastic plate and a thick poroelastic medium modeled by a Biot model. This
is the first global (weak) solution existence result in the context of poroelastic FSI. Numerical
simulations of the underlying problem showing optimal design of a bioartificial pancreas, will
be presented. If time permits, I will also preview a well-posedness results for a stochastically
perturbed FSI problem. This is a joint work with bioengineer Shuvo Roy (UCSF), and mathe-
maticians Yifan Wang (UCI), Lorena Bociu (NCSU), Boris Muha (University of Zagreb), and
Justin Webster (University of Maryland, Baltimore County). The stochastically perturbed FSI
result was obtained with PhD student Jeffrey Kuan (UC Berkeley).
498
