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Universität Augsburg
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Universität Augsburg
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Professor Dr. Markus Gahn
Universität Augsburg
spricht am
Dienstag, 13. Oktober 2026
um
16:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| Starting from a microscopic model describing fluid flow through a thin, elastic, porous membrane separating two bulk fluid domains, we rigorously derive macroscopic models where the thin layer is replaced by a lower-dimensional interface. Across this interface, the macroscopic model satisfies effective interface laws. More precisely, the microscopic geometry consists of a periodically structured membrane composed of a solid and fluid-filled pores, with characteristic thickness and periodicity of order $\varepsilon$, small compared to the size of the bulk regions. The fluid flow is described by the instationary Stokes equations for incompressible fluids, where we deal with different scalings for the viscosity within the layer. Further, we consider both rigid and elastic solid. For the latter, we consider linear elasticity with a linearized fluid-structure interaction. Further, we deal with different scalings of the elastic stress tensor, leading to qualitatively different macroscopic behavior. The derivation of the macroscopic model is based on compactness methods with respect to the two-scale convergence adapted to thin domains with oscillatory microstructure, where the membrane is asymptotically reduced to an effective interface. Across this interface, transmission conditions of Navier-slip type are derived, in particular inclduing displacement effects in the case of an elastic solid. Depending on the scaling for the elasticity tensor, the effective displacement satisfies either a membrane-type equation or a Kirchhoff-Love plate equation. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Malte Peter |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).