Asymptotic limit of linear parabolic equations with spatio-temporal degenerated potentials
| Autor: | Àlvarez-Caudevilla, Pablo, Bonnivard, Matthieu, Lemenant, Antoine |
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| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | ESAIM: COCV, Volume 26, 2020, Article Number: 50, Published online: 03 September 2020 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1051/cocv/2019023 |
| Popis: | In this paper, we observe how the heat equation in a non-cylindrical domain can arise as the asymptotic limit of a parabolic problem in a cylindrical domain, by adding a potential that vanishes outside the limit domain. This can be seen as a parabolic version of a previous work by the first and last authors, concerning the stationary case. We provide a strong convergence result for the solution by use of energetic methods and $\Gamma$-convergence technics. Then, we establish an exponential decay estimate coming from an adaptation of an argument due to B. Simon. Comment: 20 pages |
| Databáze: | arXiv |
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