Metastable dynamics for a hyperbolic variant of the mass conserving Allen-Cahn equation in one space dimension
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arXiv
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866913354551918592 |
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| author | Folino, Raffaele |
| author_facet | Folino, Raffaele |
| contents | In this paper, we consider some hyperbolic variants of the mass conserving Allen-Cahn equation, which is a nonlocal reaction-diffusion equation, introduced (as a simpler alternative to the Cahn-Hilliard equation) to describe phase separation in binary mixtures. In particular, we focus our attention on the metastable dynamics of some solutions to the equation in a bounded interval of the real line with homogeneous Neumann boundary conditions. It is shown that the evolution of profiles with $N+1$ transition layers is very slow and we derive a system of ODEs, which describes the exponentially slow motion of the layers. A comparison with the classical Allen-Cahn and Cahn-Hilliard equations and theirs hyperbolic variations is also performed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_00355 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Metastable dynamics for a hyperbolic variant of the mass conserving Allen-Cahn equation in one space dimension Folino, Raffaele Analysis of PDEs In this paper, we consider some hyperbolic variants of the mass conserving Allen-Cahn equation, which is a nonlocal reaction-diffusion equation, introduced (as a simpler alternative to the Cahn-Hilliard equation) to describe phase separation in binary mixtures. In particular, we focus our attention on the metastable dynamics of some solutions to the equation in a bounded interval of the real line with homogeneous Neumann boundary conditions. It is shown that the evolution of profiles with $N+1$ transition layers is very slow and we derive a system of ODEs, which describes the exponentially slow motion of the layers. A comparison with the classical Allen-Cahn and Cahn-Hilliard equations and theirs hyperbolic variations is also performed. |
| title | Metastable dynamics for a hyperbolic variant of the mass conserving Allen-Cahn equation in one space dimension |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1912.00355 |