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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, Hindawi, vol. 2008, pages 1-27, June.
  • Handle: RePEc:hin:jnljam:846282
    DOI: 10.1155/2008/846282
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