The heat equation with strongly singular potentials

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.

arXiv comment20 pages, 11 figures. This work is a continuation of the series of studies of authors arXiv:2004.10145, arXiv:2004.10182

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Cited by in corpus (4)

• Discrete Heat Equation with irregular thermal conductivity and tempered distributional data
• Stochastic parabolic equations with singular potentials
• Fractional Klein-Gordon equation with singular mass. II: Hypoelliptic case
• Fractional Schrödinger equations with singular potentials of higher order. II: Hypoelliptic case