Heat equation for Sturm–Liouville operator with singular propagation and potential
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Michael Ruzhansky
Abstract
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.
Funding source: Engineering and Physical Sciences Research Council
Award Identifier / Grant number: EP/V005529/1
Funding source: Ministry of Education and Science of the Republic of Kazakhstan
Award Identifier / Grant number: AP23486342
Funding statement: This research was funded by the FWO Odysseus 1 grant G.0H94.18N: Analysis and Partial Differential Equations, and by the Methusalem programme of the Ghent University Special Research Fund (BOF) (Grant number 01M01021). Michael Ruzhansky is also supported by EPSRC grant EP/V005529/1. Alibek Yeskermessuly is supported by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP23486342).
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