Wave equation for Sturm-Liouville operator with singular potentials
Ruzhansky M. Shaimardan S. Yeskermessuly A.
1 March 2024Academic Press Inc.
Journal of Mathematical Analysis and Applications
2024#531Issue 1
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.
Singular coefficient , Sturm-Liouville , Very weak solutions , Wave equation
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Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Belgium
School of Mathematical Sciences, Queen Mary University of London, United Kingdom
L.N. Gumilyov Eurasian National University, Nur-Sultan, Kazakhstan
Altynsarin Arkalyk Pedagogical Institute, Arkalyk, Kazakhstan
Department of Mathematics: Analysis
School of Mathematical Sciences
L.N. Gumilyov Eurasian National University
Altynsarin Arkalyk Pedagogical Institute
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