Multilayer heat equations and their solutions via oscillating integral transforms

By expanding the Dirac delta function in terms of eigenfunctions 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 existence a multilayer spatial structure moving (time-dependent) boundaries (internal interfaces) between layers. Thus, constructed solutions semi-analytical extend authors’ previous work (Itkin, Lipton, Muravey, Multilayer heat equations: Application FMF, 1, 2021). However, our method does not duplicate one but provides alternative representations solution have different properties serve other purposes.