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

Ruzhansky M. Yeskermessuly A.
November 2023 Springer

Bulletin of the Malaysian Mathematical Sciences Society
2023 #46 Issue 6

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.

Riemann–Lebesgue lemma , Singular coefficient , Sturm–Liouville , Very weak solutions , Wave equation

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Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom
Altynsarin Arkalyk Pedagogical Institute, Arkalyk, Kazakhstan

Department of Mathematics: Analysis
School of Mathematical Sciences
Altynsarin Arkalyk Pedagogical Institute

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