Wave equation for Sturm-Liouville operator with singular potentials

Michael Ruzhansky; Serikbol Shaimardan; Alibek Yeskermessuly

Wave equation for Sturm-Liouville operator with singular potentials

Analysis of PDEs 2022-09-20 v1

Authors: Michael Ruzhansky , Serikbol Shaimardan , Alibek Yeskermessuly

Abstract

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.

Keywords

sturm-liouville operators water waves initial-boundary value problems

Cite

@article{arxiv.2209.08278,
  title  = {Wave equation for Sturm-Liouville operator with singular potentials},
  author = {Michael Ruzhansky and Serikbol Shaimardan and Alibek Yeskermessuly},
  journal= {arXiv preprint arXiv:2209.08278},
  year   = {2022}
}