A Nonnegative Weak Solution to the Phase Field Crystal Model with Degenerate Mobility
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909177261064192 |
|---|---|
| author | Luong, Toai Wise, Steve |
| author_facet | Luong, Toai Wise, Steve |
| contents | Phase field crystal is a model used to describe the behavior of crystalline materials at the mesoscale. In this study, we investigate the well-posedness of a phase field crystal equation subject to a degenerate mobility $M(u)$ that equals zero for $u\leq 0$. First, we prove the existence of a weak solution to a phase field crystal equation with non-degenerate cutoff mobility. Then, assuming that the initial data $u_0(x)$ is positive, we establish the existence of a nonnegative weak solution to the degenerate case. Such solution is the limit of solutions corresponding to non-degenerate mobilities. We also verify that such a weak solution satisfies an energy dissipation inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13482 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Nonnegative Weak Solution to the Phase Field Crystal Model with Degenerate Mobility Luong, Toai Wise, Steve Analysis of PDEs Phase field crystal is a model used to describe the behavior of crystalline materials at the mesoscale. In this study, we investigate the well-posedness of a phase field crystal equation subject to a degenerate mobility $M(u)$ that equals zero for $u\leq 0$. First, we prove the existence of a weak solution to a phase field crystal equation with non-degenerate cutoff mobility. Then, assuming that the initial data $u_0(x)$ is positive, we establish the existence of a nonnegative weak solution to the degenerate case. Such solution is the limit of solutions corresponding to non-degenerate mobilities. We also verify that such a weak solution satisfies an energy dissipation inequality. |
| title | A Nonnegative Weak Solution to the Phase Field Crystal Model with Degenerate Mobility |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.13482 |