Asymptotic analysis of the steady stokes equation with randomly perturbed viscosity in a thin tube structure |
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Authors: | G Cardone L Carraro G R Fares G P Panasenko |
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Institution: | 1.Department of Engineering,University of Sannio,Benevento,Italy;2.Laboratory of Mathematics,University of Saint Etienne,St. Etienne,France |
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Abstract: | The Stokes equation with the nonconstant viscosity is considered in a thin tube structure, i.e., in a connected union of thin
rectangles with heights of order ε ≪ 1 and bases of order 1 with smoothened boundary. An asymptotic expansion of the solution is constructed. In the case of
random perturbations of the constant viscosity, we prove that the leading term for the velocity is deterministic, while for
the pressure it is random, but the expectations of the pressure satisfies the deterministic Darcy equation. Estimates for
the difference between the exact solution and its asymptotic approximation are proved. Bibliography: 11 titles. Illustrations:
3 figures. |
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Keywords: | |
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