title: Solution of a class of two-dimensional integral equations
abstract: The two-dimensional integral equation 1/ pi integral integral /sub D/( phi (r, theta )/R/sup 2/)dS=f(r/sub 0/, theta /sub 0/) defined on a circular disk D: r/sub 0/<or=a, 0<or= theta /sub 0/<or=2 pi , is considered in the present paper. Here R in the kernel denotes the distance between two points P(r, theta ) and P/sub 0/(r/sub 0/, theta /sub 0/) in D, and 0< alpha <2 or 2< alpha <4. Based on some known results of Bessel functions, integral representations of the kernel are established for 0< alpha <2 and 2< alpha <4, respectively, and employed to solve the corresponding two-dimensional integral equation. The solutions of the weakly singular integral equation for 0< alpha <2 and of the hypersingular integral equation for 2< alpha <4 are obtained, respectively
keyphrases: circular disk kernel Bessel functions integral representations weakly singular integral equation hypersingular integral equation 2D integral equations