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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.13592 |
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Table of 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.