Periodic convolution equations on segments which occur in elasticity theory and mathematical physics: PMM, vol. 35, n≗ 5, 1971, pp. 861–868

Abstract

Integral convolution equations given on a system of segments are considered; the kernel of the integral equation is a periodic function with period T The unique solvability of the equations is established for kernels of a general kind, an approximate factorization is given a foundation, and a method for construction of the approximate solution is also indicated. Integral equations of the kind mentioned occur in mixed problems of elasticity theory and mathematical physics, posed for finite bodies [1, 2], as well as for infinite bodies with periodic boundary conditions [3]. The result herein, just as in [4], is necessary for the correct formulation and solution of dynamic contact problems.