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

A. V. Balakrishnan and M. A. Shubov

Journal of Applied Mathematics, 2008, vol. 2008, issue 1

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.

Date: 2008
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https://doi.org/10.1155/2008/846282

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2008:y:2008:i:1:n:846282

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