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arXiv · 2112.00949

Multilayer heat equations and their solutions via oscillating integral transforms

Andrey Itkin·Alexander Lipton·Dmitry Muravey
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Abstract

By expanding the Dirac delta function in terms of the eigenfunctions of the corresponding Sturm-Liouville problem, we construct some new (oscillating) integral transforms. These transforms are then used to solve various finance, physics, and mathematics problems, which could be characterized by the existence of a multilayer spatial structure and moving (time-dependent) boundaries (internal interfaces) between the layers. Thus, constructed solutions are semi-analytical and extend the authors' previous work (Itkin, Lipton, Muravey, Multilayer heat equations: application to finance, FMF, 1, 2021). However, our new method doesn't duplicate the previous one but provides alternative representations of the solution which have different properties and serve other purposes.

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Andrey Itkin, Alexander Lipton, Dmitry Muravey. 2021-12-02. Multilayer heat equations and their solutions via oscillating integral transforms. https://doi.org/10.1016/j.physa.2022.127544

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