Solution of a class of two-dimensional integral equations

[摘要] The two-dimensional integral equation (1)/(pi) integral integral(D) phi(r,theta)/R-alpha dS = f(r(0),theta(0)) defined on a circular disk D : r(0) less than or equal to a, 0 less than or equal to theta(0) less than or equal to 2pi, is considered in the present paper. Here R in the kernel denotes the distance between two points P(r, theta) and P-0(r(0) ,theta(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. (C) 2001 Elsevier Science B.V. All rights reserved.

[发布日期] 2002-08-15

[关键词] two-dimensional integral equation;hypersingular integral equation;finite-part integral;Bessel function