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Small pertubations of an interface for Stokes system
Author(s) -
Daveau Christian,
Khelifi Abdessatar,
Oueslati Soumaya
Publication year - 2020
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201800175
Subject(s) - perturbation (astronomy) , asymptotic expansion , mathematical analysis , moment (physics) , singular perturbation , method of matched asymptotic expansions , physics , field (mathematics) , interface (matter) , mathematics , mechanics , classical mechanics , pure mathematics , boundary value problem , bubble , quantum mechanics , maximum bubble pressure method
Abstract We consider the Stokes system for a viscous medium consisting of an impurely (inclusion) merged in a consistent background medium. Appointed on both field expansion and layer potential methods, we strictly derive the asymptotic expansion of the perturbed velocity field because of small perturbations in the interface of the inclusion. We use these techniques to determine a relationship between Stokes solutions measurements and the shape of the object. Moreover, we may prove an asymptotic expansion for the perturbation in the viscosity moment tensors (VMTs) caused by the presence of small changes in the interface of the impurity.