SOLUTIONS OF THE INTEGRODIFFERENTIAL EQUATION FOR A THIN JET-FLAPPED AEROFOIL

The integro-differential equation for a thin jet-flapped aerofoil was derived by Spence (Proc. Roy. Sec., London A-238 (1956), p. 46). Its n umerical and asymptotic solutions have been obtained, but the existenc e of solutions has not been discussed yet, since the governing equatio n is singular. In the present paper, we derive an integral equation of the Fredholm type of the second kind which is not singular from the o riginal integro-differential equation. We further prove the existence and uniqueness of the solution and derive the asymptotic solutions. Co mparing with earlier works, we show that earlier asymptotic solutions obtained by the method of matched asymptotic expansions are reasonable .