The heat equation with strongly singular potentials
arXiv:2004.11255 · doi:10.1016/j.amc.2021.126006
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 physical observations.
20 pages, 11 figures. This work is a continuation of the series of studies of authors arXiv:2004.10145, arXiv:2004.10182