Multiscale analysis and homogenization of nonlocal thin films
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911656892694528 |
|---|---|
| author | Ansini, Nadia Tribuzio, Antonio |
| author_facet | Ansini, Nadia Tribuzio, Antonio |
| contents | In this paper, we introduce a nonlocal, variational model for thin films. We consider convolution-type functionals defined on a thin domain whose thickness is of order $γ$, where the effective interactions range between points is of order $\varepsilon$. We study the $Γ$-convergence of these energies, as both parameters vanish, to a local integral functional defined on a lower-dimensional domain. In the periodic homogenization setting, the limit energy density is characterized by an asymptotic formula that depends on the interplay between $\varepsilon$ and $γ$. Under suitable assumptions, this formula exhibits a separation of scales effect, namely, the limit energy can be obtained by performing two successive $Γ$-limits, first letting one parameter tend to zero while keeping the other fixed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05988 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multiscale analysis and homogenization of nonlocal thin films Ansini, Nadia Tribuzio, Antonio Analysis of PDEs 49J45, 74Q05, 45E10, 74K35 In this paper, we introduce a nonlocal, variational model for thin films. We consider convolution-type functionals defined on a thin domain whose thickness is of order $γ$, where the effective interactions range between points is of order $\varepsilon$. We study the $Γ$-convergence of these energies, as both parameters vanish, to a local integral functional defined on a lower-dimensional domain. In the periodic homogenization setting, the limit energy density is characterized by an asymptotic formula that depends on the interplay between $\varepsilon$ and $γ$. Under suitable assumptions, this formula exhibits a separation of scales effect, namely, the limit energy can be obtained by performing two successive $Γ$-limits, first letting one parameter tend to zero while keeping the other fixed. |
| title | Multiscale analysis and homogenization of nonlocal thin films |
| topic | Analysis of PDEs 49J45, 74Q05, 45E10, 74K35 |
| url | https://arxiv.org/abs/2605.05988 |