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Conformal mapping of multiply connected domains exterior to thin regions

  • Dorel Homentcovschi
Original Papers

Summary

This paper gives the formal asymptotic expansion of the functionZ=F(z, ε) which maps conformally the multiple connected domain exterior to some symmetrical thin regions inz plane into the complex planeZ with aligned cuts on the real axis.

The functionF(z, ε) is represented as a superposition of singularities on segments inside the thin regions. The resulting integral equation is integrated asymptotically by using the method developed in [1].

In the last section of the paper the given theory is applied to the conformal mapping of the domain exterior to two aligned thin ellipses.

Keywords

Integral Equation Mathematical Method Asymptotic Expansion Real Axis Conformal Mapping 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Résumé

Cet ouvrage donne le développement asymptotique formel de la fonctionZ=F(z, ε) qui transforme conformément le domaine multiplement connexe, exterieur de certaines régions symétriques minces du planz dans le plan complexeZ avec coupures alignées sur l'axe réele.

La fonctionZ=F(z, ε) est representée comme une superposition des singularités sur des segments à l'interieur des régions minces. L'équation intégrale qui en résulte est intégrée asymptotiquement à l'aide de la méthode developée en [1].

Dans la dernière section du cet article la théorie donnée est appliquée à la transformation conforme du domaine extérieur à deux ellipses minces alignées.

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References

  1. [1]
    R. A. Handelsman and J. B. Keller,Axially symmetric potential flow around a slender body. J. Fluid. Mech.28, 131–142 (1967).Google Scholar
  2. [2]
    D. Homentcovschi,Conformal mapping of the domain exterior to a thin region. SIAM J. Math. Anal.10, 1246–1258 (1978).Google Scholar
  3. [3]
    D. Homentcovschi,Conformal mapping of the domain exterior to a thin symmetrical profile. Rev. Roum. Math. Pures et Appl.,24, 1317–1326 (1979).Google Scholar
  4. [4]
    D. Homentcovschi,On the mixed boundary-value problem for harmonic functions in plane domains. Z. angew. Math. Phys.31, 352–366 (1980).Google Scholar
  5. [5]
    C. Jacob,Introduction mathématique à la mécanique des fluides. Gauthier-Villars, Bucarest-Paris, 1959.Google Scholar

Copyright information

© Birkhäuser Verlag Basel 1982

Authors and Affiliations

  • Dorel Homentcovschi
    • 1
  1. 1.Central Institute of MathematicsBukarestRoumania

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