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Existence results for a nonlinear problem modeling the displacement of a solid in a transverse flow. (English) Zbl 0820.76014

Summary: We study a simplified mathematical model that describes the stationary displacements of a solid body immersed in a transverse flow. This model involves the Laplace equation with a non-homogeneous Neumann boundary condition in a domain whose geometry depends on the displacement of the solid under the action of the fluid. The solution of the equation and the displacement are related by a nonlinear condition. The nonlinear character of the model is also present in the dependence of the domain on the solution. We give here an existence result for this case and for a more general situation.

MSC:

76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
35Q35 PDEs in connection with fluid mechanics
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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References:

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