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Bibliographic Details
Main Authors: Ruzhansky, Michael, Yeskermessuly, Alibek
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2310.09947
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Table of Contents:
  • 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.