Concerning the strong and uniform decay of solutions to coupled fluid/multilayered structure PDE dynamics

Abstract: In this talk, we will discuss our recent work on a certain multilayered structure-fluid interaction (FSI) which arises in the modeling of vascular blood flow. The coupled PDE system under our consideration mathematically accounts for the fact that mammalian veins and arteries are typically 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 elastic 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 elastic-3D elastic dynamics. For this multilayered FSI system, we will in particular present results of strong stability for finite energy solutions, and polynomial decay for sufficiently regular solutions. This is joint work with Pelin Güven Geredeli and Boris Muha.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor).