Hysteretic dynamics of phase interfaces in bilinear forward-backward diffusion equations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913323414454272 |
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| author | Herrmann, Michael Janßen, Dirk |
| author_facet | Herrmann, Michael Janßen, Dirk |
| contents | We study single-interface solutions to a free boundary problem that couples bilinear bulk diffusion to the Stefan condition and a hysteretic flow rule for phase boundaries. We introduce a time-discrete approximation scheme and establish its convergence in the limit of vanishing step size. The main difficulty in our proof are strong microscopic oscillations which are produced by a propagating phase interface and need to be controlled on the macroscopic scale. We also present numerical simulations and discuss the link to the viscous regularization of ill-posed diffusion equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13592 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hysteretic dynamics of phase interfaces in bilinear forward-backward diffusion equations Herrmann, Michael Janßen, Dirk Analysis of PDEs We study single-interface solutions to a free boundary problem that couples bilinear bulk diffusion to the Stefan condition and a hysteretic flow rule for phase boundaries. We introduce a time-discrete approximation scheme and establish its convergence in the limit of vanishing step size. The main difficulty in our proof are strong microscopic oscillations which are produced by a propagating phase interface and need to be controlled on the macroscopic scale. We also present numerical simulations and discuss the link to the viscous regularization of ill-posed diffusion equations. |
| title | Hysteretic dynamics of phase interfaces in bilinear forward-backward diffusion equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.13592 |