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A nonlocal transport problem describing pore growth
Abstract
We study a nonlocal transport problem describing pore growth in a biological membrane exposed to a periodic electric potential, where the growth term is modified through the first moment of the solution n1(t). We show that for initial data f0 with noncompact support it holds n1(t) → ∞ , whereas for f0 with compact support the limit of n1 depends sensitively on the data. For a broad class of initial data we additionally obtain n1 ∼ t1/2. In the case of a constant external potential we further prove that solutions converge to the self-similar solution having the same tail behaviour as f0.
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BibTeX
@misc{niethammer2026nonlocal,
title = {{A nonlocal transport problem describing pore growth}},
author = {Barbara Niethammer and Lorena Pohl and Juan J. L. Velázquez},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40019},
eprint = {2610.40019},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40019},
}
RIS
TY - UNPB
TI - A nonlocal transport problem describing pore growth
AU - Barbara Niethammer
AU - Lorena Pohl
AU - Juan J. L. Velázquez
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40019
UR - https://arxiv.org/abs/2610.40019
AB - We study a nonlocal transport problem describing pore growth in a biological membrane exposed to a periodic electric potential, where the growth term is modified through the first moment of the solution n_1(t). We show that for initial data f_0 with noncompact support it holds n_1(t) → ∞ , whereas for f_0 with compact support the limit of n_1 depends sensitively on the data. For a broad class of initial data we additionally obtain n_1 ∼ t^1/2. In the case of a constant external potential we further prove that solutions converge to the self-similar solution having the same tail behaviour as f_0.
ER -