PreprintCC BY 4.0arXiv
Localization properties of a free boundary problem for cell polarization
Abstract
We investigate localization in a time-dependent contrained obstacle problem for the density of an active protein on a cell membrane. This free boundary problem has been derived in Logioti et al. [17] as a model for cell polarization under the influence of an external signal. We show that in the limit of small mass there is instantaneous localization, that is the mass of the active protein concentrates in the set where the signal is maximal for any positive time t>0. We give a precise a characterization of this concentration process on the appropriate slow time scale and illustrate this for a few examples of the external signal.
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BibTeX
@misc{niethammer2026localization,
title = {{Localization properties of a free boundary problem for cell polarization}},
author = {B. Niethammer and M. Röger and J. J. L. Velázquez},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20609},
eprint = {2609.20609},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20609},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Localization properties of a free boundary problem for cell polarization
AU - B. Niethammer
AU - M. Röger
AU - J. J. L. Velázquez
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20609
UR - https://arxiv.org/abs/2609.20609
AB - We investigate localization in a time-dependent contrained obstacle problem for the density of an active protein on a cell membrane. This free boundary problem has been derived in Logioti et al. [17] as a model for cell polarization under the influence of an external signal. We show that in the limit of small mass there is instantaneous localization, that is the mass of the active protein concentrates in the set where the signal is maximal for any positive time t>0. We give a precise a characterization of this concentration process on the appropriate slow time scale and illustrate this for a few examples of the external signal.
ER -