The heat equation with strongly singular potentials
Altybay A. Ruzhansky M. Sebih M.E. Tokmagambetov N.
15 June 2021Elsevier Inc.
Applied Mathematics and Computation
2021#399
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.
Delta function , Distributional coefficient , Generalised solution , Heat equation , Mollifier , Numerical analysis , Regularisation , Singular potential
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Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Belgium
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
School of Mathematical Sciences, Queen Mary University of London, United Kingdom
Laboratory of Analysis and Control of Partial Differential Equations, Djillali Liabes University, Sidi Bel Abbes, Algeria
Laboratory of Geomatics, Ecology and Environment, University Mustapha Stambouli of Mascara, Algeria
Al-Farabi Kazakh National University, Almaty, Kazakhstan
Department of Mathematics: Analysis
Institute of Mathematics and Mathematical Modeling
School of Mathematical Sciences
Laboratory of Analysis and Control of Partial Differential Equations
Laboratory of Geomatics
Al-Farabi Kazakh National University
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