Heat equation for Sturm–Liouville operator with singular propagation and potential

Ruzhansky M. Yeskermessuly A.
1 December 2025 Walter de Gruyter GmbH

Journal of Applied Analysis
2025 #31 Issue 2 311 - 328 pp.

This article considers the initial boundary value problem for the heat equation with the time-dependent Sturm–Liouville operator with singular potentials. To obtain a solution by the method of separation of variables, the problem is reduced to the problem of eigenvalues of the Sturm–Liouville operator. Further on, the solution to the initial boundary value problem is constructed in the form of a Fourier series expansion. A heterogeneous case is also considered. Finally, we establish the well-posedness of the equation in the case when the potential and initial data are distributions, also for singular time-dependent coefficients.

Heat equation , singular potential , singular propagation , Sturm–Liouville , very weak solutions

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

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

10 лет помогаем публиковать статьи Международный издатель

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