Very Weak Solution of the Wave Equation for Sturm-Liouville Operator

We considered the initial-boundary value problem for the wave equation with the Sturm-Liouville operator with singular coefficients. The method of separation of variables is used to construct the solution. The homogeneous and non-homogeneous cases of the equation are considered. Finally, existence, uniqueness, and consistency theorems are given for a very weak solution of the wave equation with singular coefficients in a bounded domain.