Wave Equation for Sturm-Liouville Operator with Singular Intermediate Coefficient and Potential

In this paper, we consider a wave equation on a bounded domain with a Sturm-Liouville operator with a singular intermediate coefficient and a singular potential. To obtain and evaluate the solution, the method of separation of variables is used, then the expansion in the Fourier series in terms of the eigenfunctions of the Sturm-Liouville operator is used. The Sturm-Liouville eigenfunctions are determined by such coefficients using the modified Prufer transform. Existence, uniqueness and consistency theorems are also proved for a very weak solution of the wave equation with singular coefficients.

Automated summary

This paper considers a wave equation on a bounded domain with a Sturm-Liouville operator with singular intermediate coefficient and singular potential. The method of separation of variables is used to obtain and evaluate the solution, followed by expansion in the Fourier series using the eigenfunctions of the Sturm-Liouville operator. The Sturm-Liouville eigenfunctions are determined using the modified Prufer transform. Existence, uniqueness, and consistency theorems are proved for a very weak solution of the wave equation with singular coefficients.