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An integral equation of the first kind for a free boundary value problem of the stationary Stokes' equations
Author(s) -
Hebeker F. K.,
Nedelec J. C.
Publication year - 1987
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670090135
Subject(s) - mathematics , boundary value problem , mathematical analysis , jump , integral equation , free boundary problem , representation (politics) , boundary (topology) , partial differential equation , differential equation , integro differential equation , first order partial differential equation , law , physics , quantum mechanics , politics , political science
We investigate a free boundary value problem of the stationary Stokes' equations. In a previous paper adapted hydrodynamical potentials have been constructed and their jump relations have been discussed. Here we study a direct method to obtain an equivalent boundary integral equations' system of the first kind. Its solution properties are investigated in the framework of strongly elliptic pseudodifferential operators. For numerical purposes a suitable representation formula for the variational equation is given in terms of integro‐differential operators which avoids the evaluation of hypersingular integrals.

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