Classical and Generalized Solutions of a Mixed Problem for a Nonhomogeneous Wave Equation

Abstract

A.N. Krylov’s ideas concerning convergence acceleration for Fourier series are used to obtain explicit expressions for the classical solution of a mixed problem for a nonhomogeneous equation and explicit expressions for a generalized solution in the case of arbitrary summable \(q(x)\), \(\varphi (x)\), \(\psi (x)\), and \(f(x,t)\).