| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 50 | |
| Number of page(s) | 20 | |
| DOI | https://doi.org/10.1051/cocv/2019023 | |
| Published online | 03 September 2020 | |
Asymptotic limit of linear parabolic equations with spatio-temporal degenerated potentials
Universite Paris Diderot,
Paris, France.
* Corresponding author: lemenant@ljll.univ-paris-diderot.fr
Received:
9
April
2018
Accepted:
7
April
2019
In this paper, we observe how the heat equation in a noncylindrical 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 [Alvarez-Caudevilla and Lemenant, Adv. Differ. Equ. 15 (2010) 649-688]. We provide a strong convergence result for the solution by use of energetic methods and Γ-convergence technics. Then, we establish an exponential decay estimate coming from an adaptation of an argument due to B. Simon.
Mathematics Subject Classification: 35A05 / 35A15
Key words: Parabolic problems / Gamma-convergence / energetic methods / variational methods / partial differential equations
© The authors. Published by EDP Sciences, SMAI 2020
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