The heat equation with strongly singular potentials
| Autor: | Mohammed Elamine Sebih, Michael Ruzhansky, Niyaz Tokmagambetov, Arshyn Altybay |
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| Přispěvatelé: | Engineering & Physical Science Research Council (EPSRC) |
| Rok vydání: | 2021 |
| Předmět: |
0209 industrial biotechnology
0103 Numerical and Computational Mathematics Applied Mathematics Weak solution Mathematical analysis Numerical & Computational Mathematics Computational mathematics 020206 networking & telecommunications 02 engineering and technology Sense (electronics) 35D99 35K67 34A45 Computational Mathematics Mathematics - Analysis of PDEs 020901 industrial engineering & automation Consistency (statistics) 0102 Applied Mathematics FOS: Mathematics 0202 electrical engineering electronic engineering information engineering Heat equation Uniqueness Laser heating Analysis of PDEs (math.AP) 0802 Computation Theory and Mathematics Mathematics Sign (mathematics) |
| Zdroj: | Applied Mathematics and Computation. 399:126006 |
| ISSN: | 0096-3003 |
| DOI: | 10.1016/j.amc.2021.126006 |
| Popis: | 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 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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