A phase-field model for the Verigin problem: weak solutions and sharp-interface limit
Abstract
We introduce a novel phase-field model approximating the Verigin problem with phase transition. For fixed interface thickness ε>0, we construct weak solutions through a time-discrete variational scheme combining a Wasserstein minimizing-movement for the density with Schätzle's selection procedure for the phase field, which yields strong compactness and an almost-minimizing property. We then investigate the sharp-interface limit ε ↓0. For well-prepared initial data, we establish strong compactness of the densities and phase fields, and we prove convergence of the time-integrated diffuse interfacial energy to the perimeter. The limiting evolution is identified as a weak solution of the Verigin problem with phase transition, satisfying an optimal energy dissipation inequality.
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BibTeX
@misc{kubin2026phasefield,
title = {{A phase-field model for the Verigin problem: weak solutions and sharp-interface limit}},
author = {Anna Kubin and Alice Marveggio},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30412},
eprint = {2609.30412},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30412},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A phase-field model for the Verigin problem: weak solutions and sharp-interface limit
AU - Anna Kubin
AU - Alice Marveggio
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30412
UR - https://arxiv.org/abs/2609.30412
AB - We introduce a novel phase-field model approximating the Verigin problem with phase transition. For fixed interface thickness ε>0, we construct weak solutions through a time-discrete variational scheme combining a Wasserstein minimizing-movement for the density with Schätzle's selection procedure for the phase field, which yields strong compactness and an almost-minimizing property. We then investigate the sharp-interface limit ε ↓0. For well-prepared initial data, we establish strong compactness of the densities and phase fields, and we prove convergence of the time-integrated diffuse interfacial energy to the perimeter. The limiting evolution is identified as a weak solution of the Verigin problem with phase transition, satisfying an optimal energy dissipation inequality.
ER -