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Reduction of Boundary Value Problem to Possio Integral Equation in Theoretical Aeroelasticity

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  • A. V. Balakrishnan
  • M. A. Shubov

Abstract

The present paper is the first in a series of works devoted to the solvability of the Possio singular integral equation. This equation relates the pressure distribution over a typical section of a slender wing in subsonic compressible air flow to the normal velocity of the points of a wing (downwash). In spite of the importance of the Possio equation, the question of the existence of its solution has not been settled yet. We provide a rigorous reduction of the initial boundary value problem involving a partial differential equation for the velocity potential and highly nonstandard boundary conditions to a singular integral equation, the Possio equation. The question of its solvability will be addressed in our forthcoming work.

Suggested Citation

  • A. V. Balakrishnan & M. A. Shubov, 2008. "Reduction of Boundary Value Problem to Possio Integral Equation in Theoretical Aeroelasticity," Journal of Applied Mathematics, John Wiley & Sons, vol. 2008(1).
    • Handle: RePEc:wly:jnljam:v:2008:y:2008:i:1:n:846282
    DOI: 10.1155/2008/846282
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    References listed on IDEAS

    as
    1. Ricardo Estrada & Ram P. Kanwal, 2000. "Distributional Solutions of Singular Integral Equations," Springer Books, in: Singular Integral Equations, chapter 5, pages 175-249, Springer.
    2. Ricardo Estrada & Ram P. Kanwal, 2000. "Singular Integral Equations," Springer Books, Springer, number 978-1-4612-1382-6, March.
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