Asymptotic limit of linear parabolic equations with spatio-temporal degenerated potentials
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911764648558592 |
|---|---|
| author | Àlvarez-Caudevilla, Pablo Bonnivard, Matthieu Lemenant, Antoine |
| author_facet | Àlvarez-Caudevilla, Pablo Bonnivard, Matthieu Lemenant, Antoine |
| contents | 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 $Γ$-convergence technics. Then, we establish an exponential decay estimate coming from an adaptation of an argument due to B. Simon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14249 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic limit of linear parabolic equations with spatio-temporal degenerated potentials Àlvarez-Caudevilla, Pablo Bonnivard, Matthieu Lemenant, Antoine Analysis of PDEs 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 $Γ$-convergence technics. Then, we establish an exponential decay estimate coming from an adaptation of an argument due to B. Simon. |
| title | Asymptotic limit of linear parabolic equations with spatio-temporal degenerated potentials |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.14249 |