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A two-dimensional time dependent model of an interaction between a thin elastic plate and a Newtonian viscous fluid described by the non-steady Stokes equations is considered. It depends on a small parameter ε that is the ratio of the thicknesses of the plate and the fluid layer. The Young's modulus of the plate and its density may be great or small parameters equal to some powers (positive or negative) of ε while the density and the viscosity of the fluid are supposed to be of order one. An asymptotic expansion is constructed and justified for various magnitudes of the rigidity and density of the plate. The limit problems are studied in all these cases. They are Stokes equations with some special coupled or uncoupled boundary conditions modeling the interaction with the plate. The estimates of the difference between the exact solution and a truncated asymptotic expansion are established. These estimates justify the asymptotic approximations. [ABSTRACT FROM AUTHOR]

A periodic, axially symmetric time-dependent model of interaction between a viscous fluid and a thin cylindrical elastic tube is considered. The problem depends on a small parameter , representing the ratio of the thickness of the wall and the radius of the cylinder. We consider Young's modulus of the elastic medium and its density great or small parameters equal to some powers of . An asymptotic expansion is constructed for various magnitudes of the rigidity and of the density of the elastic tube. The generality of the considered model requires to take into account six different combinations of the three parameters depending on . We obtain in this way different limit problems which are Stokes equations with some special boundary conditions. The expansion is justified by the high-order estimates for the difference of the exact solution and truncated asymptotic approximation. [ABSTRACT FROM AUTHOR]