arXiv subjects

Lorena Pohl

Publications and source records attributed to Lorena Pohl.

2 recordsLinked to original sources

arXiv2026

Long-time behaviour of a nonlocal model for electroporation

In this paper we analyze a model for electroporation, a biological process in which a cell membrane exposed to an external voltage becomes permeable due to the formation and growth of nanoscale membrane pores. We prove a local stability result for asymptotic self-similar solutions with a power-law tail. Our method relies on the analysis of an equation for the first moment as well as comparison of solutions of the full problem to solutions of a corresponding transport problem. In particular this shows that the transport term drives the long-time behaviour.

math.AP↗

arXiv2023

A Becker-D\"oring type model for cell polarization

We propose a model for cell polarization based on the Becker-D\"oring equations with the first coagulation coefficient equal to zero. We show convergence to equilibrium for power-law coagulation and fragmentation rates and obtain a loss of mass in the limit $t \rightarrow \infty$ depending on the initial mass and the relative strengths of the coagulation and fragmentation processes. In the case of linear rates, we further show that large clusters evolve in a self-similar manner at large times by comparing limits of appropriately rescaled solutions in different spaces.

math.AP↗