Asymptotically self-similar graph-like solutions to a multi-dimensional surface diffusion flow equation under contact angle and no-flux boundary conditions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917272446042112 |
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| author | Giga, Yoshikazu Katayama, Sho |
| author_facet | Giga, Yoshikazu Katayama, Sho |
| contents | This paper studies Mullins' model of thermal grooving which consists of a surface diffusion flow equation with contact angle and no-flux boundary conditions. We consider this problem in a multi-dimensional half space and prove that if the slope of the initial data is close to that consistent with the contact angle, then there exists a unique global-in-time solution. In particular, we show the existence of a self-similar solution for a given behavior at the space infinity. We also show that our global solution converges to a self-similar solution as the time tends to infinity if the initial data is asymptotically homogeneous at the space infinity. No assumption on the size of the contact angle is imposed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12619 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotically self-similar graph-like solutions to a multi-dimensional surface diffusion flow equation under contact angle and no-flux boundary conditions Giga, Yoshikazu Katayama, Sho Analysis of PDEs 35K61, 35C06, 35K59, 35Q79, 53E40 This paper studies Mullins' model of thermal grooving which consists of a surface diffusion flow equation with contact angle and no-flux boundary conditions. We consider this problem in a multi-dimensional half space and prove that if the slope of the initial data is close to that consistent with the contact angle, then there exists a unique global-in-time solution. In particular, we show the existence of a self-similar solution for a given behavior at the space infinity. We also show that our global solution converges to a self-similar solution as the time tends to infinity if the initial data is asymptotically homogeneous at the space infinity. No assumption on the size of the contact angle is imposed. |
| title | Asymptotically self-similar graph-like solutions to a multi-dimensional surface diffusion flow equation under contact angle and no-flux boundary conditions |
| topic | Analysis of PDEs 35K61, 35C06, 35K59, 35Q79, 53E40 |
| url | https://arxiv.org/abs/2602.12619 |