Advances in Differential Equations

Solvability of reduced Possio integral equation in theoretical aeroelasticity

Marianna A. Shubov

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This paper is concerned with the solvability of the reduced version of the Possio singular integral equation, which plays a fundamental role in theoretical aeroelasticity. This equation relates the pressure distribution over a typical section of a long slender wing in subsonic compressible air flow to the normal velocity of the points of a wing (down-wash). In spite of the importance of the Possio equation, the question of the existence of its solution has not yet been settled. In this paper, we provide a rigorous study of the reduced version of the Possio equation and prove its solvability. The reduced Possio equation is important in its own right for two reasons: (a) it can be used as an approximate equation for the numerical analysis of the coupled system describing a vibrating wing in a surrounding air flow; (b) its analysis is essential for identifying analytical difficulties associated with the general Possio equation.

Article information

Adv. Differential Equations, Volume 15, Number 9/10 (2010), 801-828.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 44N20 45A05: Linear integral equations 47G10: Integral operators [See also 45P05] 74N10: Displacive transformations


Shubov, Marianna A. Solvability of reduced Possio integral equation in theoretical aeroelasticity. Adv. Differential Equations 15 (2010), no. 9/10, 801--828.

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