Reduction ofBoundary Value Problem to Possio Integral Equation in TheoreticalAeroelasticity

Abstract

The present paper is the first in a series of works devoted to the solvability of thePossio singular integral equation. This equation relates the pressure distribution over atypical section of a slender wing in subsonic compressible air flow to the normal velocityof 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 arigorous reduction of the initial boundary value problem involving a partial differentialequation for the velocity potential and highly nonstandard boundary conditions to asingular integral equation, the Possio equation. The question of its solvability will beaddressed in our forthcoming work.