Wave equation for Sturm-Liouville operator with singular intermediate coefficient and potential

Autor:	Ruzhansky, Michael, Yeskermessuly, Alibek
Rok vydání:	2022
Předmět:	Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	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. Comment: 35 pages. arXiv admin note: substantial text overlap with arXiv:2209.08278
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2210.02789 Zobrazit plný text záznamu View this record from Arxiv