Advertisement

Journal of engineering physics

, Volume 50, Issue 6, pp 741–747 | Cite as

Solution of a Dirichlet problem in a crescent-shaped domain

  • V. I. Vlasov
Article

Abstract

We present a solution of a Dirichlet problem for the Laplace equation in a crescentshaped domain and apply this solution to some stationary problems of heat conduction, electrostatics, and the theory of elasticity.

Keywords

Statistical Physic Heat Conduction Stationary Problem Dirichlet Problem Laplace Equation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    V. I. Vlasov and A. P. Prudnikov, “Asymptotics of the solutions of some problems for the Laplace equation with deformation of a domain,” in: Modern Problems of Mathematics, Vol. 20 [in Russian] (Advances in Science and Engineering, VINITI, Academy of Sciences of the USSR), Moscow (1982), pp. 3–36.Google Scholar
  2. 2.
    Ya. S. Uflyand, Bipolar Coordinates in the Theory of Elasticity [in Russian], GITTL, Moscow-Leningrad (1950).Google Scholar
  3. 3.
    Hu Hai-Chang, “Torsion of prisms bounded by two intersecting circular cylinders,” Acta Phys. Sinica,9, No. 4, 238–254 (1953).Google Scholar
  4. 4.
    T. H. Gronwall, “On the influence of keyways of the stress distribution in cylindrical shafts,” Trans. Am. Math. Soc.,20, No. 3, 234–244 (1919).Google Scholar
  5. 5.
    S. P. Timoshenko, Theory of Elasticity, McGraw-Hill, New York (1934).Google Scholar
  6. 6.
    I. S. Sokolnikoff and E. S. Sokolnikoff, “Torsion of regions bounded by circular arcs,” Bull. Am. Math. Soc.,44, No. 3, 384–387 (1938).Google Scholar
  7. 7.
    Ya. I. Burak, Some Problems of Torsion in the Bending of Prismatic Rods [in Ukrainian], Vid. Akad. Nauk UkrRSR, Kiev (1959).Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • V. I. Vlasov
    • 1
  1. 1.Computing CenterAcademy of Sciences of the USSRMoscow

Personalised recommendations