Multilayer heat equations and their solutions via oscillating integral transforms

Andrey Itkin, Alexander Lipton and Dmitry Muravey

Physica A: Statistical Mechanics and its Applications, 2022, vol. 601, issue C

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 does not duplicate the previous one but provides alternative representations of the solution which have different properties and serve other purposes.

Keywords: Multilayer diffusion; Oscillating integral transforms; Time-dependent models; Time-dependent boundaries; Semi-analytical solution; Applications to finance and physics (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:601:y:2022:i:c:s0378437122003806

DOI: 10.1016/j.physa.2022.127544

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