Reduction of boundary value problem to Possio integral equation in theoretical aeroelasticity (Q937498)

Summary: The present paper is the first in a series of works devoted to the solvability of 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 the wing (downwash). In spite of the importance of 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.