A fluid-structure interaction model with interior damping and delay in the structure. (English) Zbl 1341.74054
Let a viscous fluid occupies a domain \(\Omega_f \subset \mathbb R^d\) (\(d=2,3\)) which encloses an elastic body occupying \(\Omega_s \subset \mathbb R^d\). The interface \(\Gamma_s\) and the outer boundary \(\Gamma_f\) are supposed to be sufficiently smooth. The author considers the Stokes equations in \(\Omega_f\) and the wave equation in \(\Omega_s\) coupled via linear conjugation conditions on \(\Gamma_s\). Spectral properties and exponential or strong stability of the interaction model under appropriate conditions on the damping factor, delay factor and the delay parameter are established using a generalized Lax-Milgram method.
Reviewer: Vladimir Mityushev (Kraków)
MSC:
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 76D07 | Stokes and related (Oseen, etc.) flows |
| 93D15 | Stabilization of systems by feedback |
| 93D20 | Asymptotic stability in control theory |
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