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arXiv · 2610.40019

A nonlocal transport problem describing pore growth

Barbara Niethammer·Lorena Pohl·Juan J. L. Velázquez
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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 $n_1(t)$. We show that for initial data $f_0$ with noncompact support it holds $n_1(t) \rightarrow \infty$ , 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 $n_1 \sim t^{\frac{1}{2}}$. 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 $f_0$.

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Barbara Niethammer, Lorena Pohl, Juan J. L. Velázquez. 2026-10-29. A nonlocal transport problem describing pore growth. https://arxiv.org/abs/2610.40019

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