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Homogenization of a lubrication problem in oscillating domain by two-scale convergence method
Buletinul Academiei de Ştiinţe a Republicii Moldova. 2021. No. 1-2. P. 31–68.
Королев А. В., Koroleva Y.
In present paper we do a homogenization with respect to a small parameter of a boundary-value problem describing fluid flow between two moving in space and time rough surfaces. The two-scale convergence method was used to justify the behavior of the flow in the limit.
Language:
English
Keywords: homogenization
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Added: October 30, 2020
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Kazeev V., Oseledets I., Rakhuba M. et al., / Series math "arxiv.org". 2020.
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