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Creative Commons Attribution 3.0 License
This work is licensed under a Creative Commons Attribution 3.0 License.

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. Copyright (C) 2008 A. V. Balakrishnan and M. A. Shubov.

Publication Date

2008

Journal Title

Journal of Applied Mathematics

Publisher

Hindawi

Digital Object Identifier (DOI)

10.1155/2008/846282

Document Type

Article

Rights

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.

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