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