Granular media equation with double-well external landscape: limiting steady state
In this paper, we give a simple condition on the initial state of the granular media equation which ensures that the limit as the time goes to infinity is the unique steady state with positive center of mass. To do so, we use functional inequalities, Laplace method and McKean–Vlasov diffusion (which...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2024-09-01
|
| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.595/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1825206275110076416 |
|---|---|
| author | Tugaut, Julian |
| author_facet | Tugaut, Julian |
| author_sort | Tugaut, Julian |
| collection | DOAJ |
| description | In this paper, we give a simple condition on the initial state of the granular media equation which ensures that the limit as the time goes to infinity is the unique steady state with positive center of mass. To do so, we use functional inequalities, Laplace method and McKean–Vlasov diffusion (which corresponds to the probabilistic interpretation of the granular media equation). |
| format | Article |
| id | doaj-art-ec96eda8d9d143df83554a469c116814 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-ec96eda8d9d143df83554a469c1168142025-02-07T11:22:28ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-09-01362G777577810.5802/crmath.59510.5802/crmath.595Granular media equation with double-well external landscape: limiting steady stateTugaut, Julian0https://orcid.org/0000-0001-9060-653XUniversité Jean Monnet, CNRS UMR 5208, Institut Camille Jordan, Maison de l’Université, 10 rue Tréfilerie, CS 82301, 42023 Saint-Étienne Cedex 2, FranceIn this paper, we give a simple condition on the initial state of the granular media equation which ensures that the limit as the time goes to infinity is the unique steady state with positive center of mass. To do so, we use functional inequalities, Laplace method and McKean–Vlasov diffusion (which corresponds to the probabilistic interpretation of the granular media equation).https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.595/ |
| spellingShingle | Tugaut, Julian Granular media equation with double-well external landscape: limiting steady state Comptes Rendus. Mathématique |
| title | Granular media equation with double-well external landscape: limiting steady state |
| title_full | Granular media equation with double-well external landscape: limiting steady state |
| title_fullStr | Granular media equation with double-well external landscape: limiting steady state |
| title_full_unstemmed | Granular media equation with double-well external landscape: limiting steady state |
| title_short | Granular media equation with double-well external landscape: limiting steady state |
| title_sort | granular media equation with double well external landscape limiting steady state |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.595/ |
| work_keys_str_mv | AT tugautjulian granularmediaequationwithdoublewellexternallandscapelimitingsteadystate |