Mixed problem for the inhomogeneous wave equation with a summable potential

Abstract

The resolvent approach to the Fourier method is used to examine the behavior of the formal solution to the mixed problem for an inhomogeneous wave equation with a summable potential. A classical solution is obtained under minimum conditions imposed on the initial function. It is shown that, in the case of square summable initial and driving functions, the series sum of the formal solution is a weak solution of the mixed problem.