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September/October 2010 Solvability of reduced Possio integral equation in theoretical aeroelasticity
Marianna A. Shubov
Adv. Differential Equations 15(9/10): 801-828 (September/October 2010).

Abstract

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.

Citation

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Marianna A. Shubov. "Solvability of reduced Possio integral equation in theoretical aeroelasticity." Adv. Differential Equations 15 (9/10) 801 - 828, September/October 2010.

Information

Published: September/October 2010
First available in Project Euclid: 18 December 2012

zbMATH: 1286.45001
MathSciNet: MR2677420

Subjects:
Primary: 44N20, 45A05, 47G10, 74N10

Rights: Copyright © 2010 Khayyam Publishing, Inc.

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Vol.15 • No. 9/10 • September/October 2010
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