A transmission problem for fluid-structure interaction in the exterior of a thin domain. (English) Zbl 1096.74014

Summary: We study the behavior of weak solutions to a time-harmonic fluid-structure interaction problem in the exterior of a thin, elastic domain, in the limit of vanishing thickness. Boundary integral operators are used to reduce the exterior problem. Formal asymptotic expansions are developed and justified. The asymptotic procedure involves the soluiton of the reduced exterior problem. Exact representation formulae for elastic displacements in the thin domain are also provided.


74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)