Retarded potentials and Laguerre transform for initial-boundary value problems for the wave equation

Abstract

Generalized solutions of initial-boundary value problems for the wave equation are investigated in this article by using retarded layer potentials and Laguerre transform with respect to the time variable. Coefficients of Fourier-Laguerre expansion for densities of potentials are obtained in explicit form. As a result, integral equations in time domain were reduced to sequences of boundary integral equations with the same boundary operator on the left-hand side.