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 $$f(x,t)$$ .