Journal of Applied Mathematics
Volume 2008 (2008), Article ID 846282, 27 pages
doi:10.1155/2008/846282
Research Article
Reduction of Boundary Value Problem to Possio Integral Equation in Theoretical Aeroelasticity
1Electrical Engineering Department, University of California, Los Angeles, CA 90095, USA
2Department of Mathematics and Statistics, University of New Hampshire, Durham, NH 03824, USA
Received 9 January 2008; Accepted 25 May 2008
Academic Editor: Bernard Geurts
Copyright © 2008 A. V. Balakrishnan and M. A. Shubov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The present paper is the first in a series of works devoted to the solvability of the
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 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 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.