Local asymptotics for the nonlocal Swift-Hohenberg equation
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908626844647424 |
|---|---|
| author | Davoli, Elisa Kuehn, Christian Scarpa, Luca Trussardi, Lara |
| author_facet | Davoli, Elisa Kuehn, Christian Scarpa, Luca Trussardi, Lara |
| contents | The nonlocal-to-local asymptotics investigation for evolutionary problems is a central topic both in the theory of PDEs and in functional analysis. More recently, it became the main core of the mathematical analysis of phase-separation models. In this paper we focus on the Swift-Hohenberg equations which are key benchmark models in pattern formation problems and amplitude equations. We prove well-posedness of the nonlocal Swift-Hohenberg equation, and study the nonlocal-to-local asymptotics with one and two nonlocal contributions under homogeneous Neumann boundary conditions using suitable energy estimates on the nonlocal problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02341 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local asymptotics for the nonlocal Swift-Hohenberg equation Davoli, Elisa Kuehn, Christian Scarpa, Luca Trussardi, Lara Analysis of PDEs The nonlocal-to-local asymptotics investigation for evolutionary problems is a central topic both in the theory of PDEs and in functional analysis. More recently, it became the main core of the mathematical analysis of phase-separation models. In this paper we focus on the Swift-Hohenberg equations which are key benchmark models in pattern formation problems and amplitude equations. We prove well-posedness of the nonlocal Swift-Hohenberg equation, and study the nonlocal-to-local asymptotics with one and two nonlocal contributions under homogeneous Neumann boundary conditions using suitable energy estimates on the nonlocal problems. |
| title | Local asymptotics for the nonlocal Swift-Hohenberg equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.02341 |