Method for Determining Power-Type Complex Singularitiesin Solutions of Singular Integral Equations with Generalized Kernelsand Complex Conjugate Unknowns

摘要

We develop a method for determining power-type complex singularities of solutionsfor a class of one-dimensional singular integral equations with generalized kernels and complexconjugate unknown functions. By analyzing the characteristic part of a singular integral equation,we reduce the problem of determining the solution singularity exponents at the ends of the integra-tion interval to two independent transcendental equations for these exponents. We show that thedistribution of admissible singularity exponents is of continuous character. We present numericalresults for a two-dimensional elasticity problem whose mathematical statement leads to a singularintegral equation of the class under study. We also reveal the drawbacks of one classical approach tothe determination of stress field singularities.