  The paper is denoted to the initial-boundary value problem for the wave
equation with the Sturm-Liouville operator with irregular (distributive)
potentials. To obtain a solution to the equation, the separation method and
asymptotics of the eigenvalues and eigenfunctions of the Sturm-Liouville
operator are used. Homogeneous and inhomogeneous cases of the equation are
considered. Next, existence, uniqueness, and consistency theorems for a very
weak solution of the wave equation with singular coefficients are proved.
