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Hebeker, F. K.

An integral equation of the first kind for a free boundary value problem of the stationary Stokes’ equations. (English) Zbl 0656.76031

Math. Methods Appl. Sci. 9, 550-575 (1987).
A direct method for obtaining an equivalent boundary integral equations’ system of first kind is created.
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. Following Bamberger’s idea for shifting by means of Fourier transformation, this approach is successful in this case with certain refinements, which are required for the three-dimensional free Stokes’ problem compared with his two-dimensional elastic waves. According to this case for numerical evaluation of the bilinear-form a new tool (due to Bamberger in case of two-dimensional elastic waves) is utilized.
Reviewer: S.Spassov

Cited in 2 Documents

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
35Q99 Partial differential equations of mathematical physics and other areas of application
76D08 Lubrication theory

Keywords:

boundary integral equations’ system of first kind; integro-differential operators; hypersingular integrals; Fourier transformation; Stokes’ problem
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\textit{F. K. Hebeker}, Math. Methods Appl. Sci. 9, 550--575 (1987; Zbl 0656.76031)
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