The heat equation with strongly singular potentials

Arshyn Altybay, Michael Ruzhansky, Mohammed Elamine Sebih and Niyaz Tokmagambetov

Applied Mathematics and Computation, 2021, vol. 399, issue C

Abstract: In this paper we consider the heat equation with strongly singular potentials and prove that it has a ”very weak solution”. Moreover, we show the uniqueness and consistency results in some appropriate sense. The cases of positive and negative potentials are studied. Numerical simulations are done: one suggests so-called ”laser heating and cooling” effects depending on a sign of the potential. The latter is justified by the physical observations.

Keywords: Heat equation; Singular potential; Generalised solution; Regularisation; Mollifier; Numerical analysis; Distributional coefficient; Delta function (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:399:y:2021:i:c:s0096300321000540

DOI: 10.1016/j.amc.2021.126006

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