Abstract
The present paper is devoted to the construction and investigation of two-dimensional hierarchical models for solid-fluid interaction. Applying the variational approach, the three-dimensional initial-boundary value problem is reduced to a sequence of two-dimensional problems and the existence and uniqueness of their solutions in suitable functional spaces is proved. The convergence of the sequence of vector-functions of three space variables to the solution of the original problem is proved and under additional regularity conditions the rate of approximation is estimated.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 51, Differential Equations and Their Applications, 2008.
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Gordeziani, D., Avalishili, M. & Avalishili, G. Dynamical two-dimensional models of solid-fluid interaction. J Math Sci 157, 16–42 (2009). https://doi.org/10.1007/s10958-009-9304-7
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DOI: https://doi.org/10.1007/s10958-009-9304-7