Long-time behaviour of a nonlocal model for electroporation

TL;DR

This paper investigates the long-term dynamics of a nonlocal mathematical model for electroporation, demonstrating that transport processes govern the asymptotic behavior of cell membrane permeability changes.

Contribution

It provides a stability analysis of self-similar solutions and highlights the role of transport in the model's long-time behavior.

Findings

Proves local stability of self-similar solutions with a power-law tail.

Shows transport term drives the long-time behavior of the model.

Uses analysis of the first moment and comparison with transport solutions.

Abstract

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.