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Fluid-structure interaction problems. (English) Zbl 0998.74028

Bonnet, M. (ed.) et al., Mathematical aspects of boundary element methods. Minisymposium during the IABEM 98 conference, dedicated to Vladimir Maz’ya on the occasion of his 60th birthday on 31st December 1997, Paris, France, 1998. Boca Raton, FL: Chapman & Hall/CRC. Chapman Hall/CRC Res. Notes Math. 414, 252-262 (2000).
The authors study the interaction of fluid with some physical structures, assuming that the problems under investigation satisfy a cone condition. The authors assume that the fluid is anisotropic and inviscid, and the solid immersed in it is anisotropic. The fluid-structure interaction is investigated when a harmonic wave propagates in the fluid. The authors apply the so-called non-local approach which is a coupling of boundary integral equation method and functional-variational methods. For that purpose, they first derived generalized Steklov-Poincaré relations between Dirichlet and Neumann data for exterior scalar field. Secondly, by applying the Green’s identity for elastic field in a bounded domain and taking into account the transmission conditions and the Steklov-Poincaré formulae on the interfaces, the authors derive an equivalent weak functional-variational formulation in a bounded domain for the original generalized fluid-structure interaction problem. Then, by applying functional-variational approach, the authors obtained necessary and sufficient conditions for solvability of the general interface problem.
For the entire collection see [Zbl 0924.00038].

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74H20 Existence of solutions of dynamical problems in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)
74E10 Anisotropy in solid mechanics
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