On the convergence of the formal Fourier solution of the wave equation with a summable potential

Abstract

The convergence of the formal Fourier solution to a mixed problem for the wave equation with a summable potential is analyzed under weaker assumptions imposed on the initial position u(x, 0) = φ(x) than those required for a classical solution up to the case φ(x) ∈ Lp[0,1] for p > 1. It is shown that the formal solution series always converges and represents a weak solution of the mixed problem.