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arXiv · 2308.04983

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

Lorena Pohl·Barbara Niethammer
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Abstract

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.

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Lorena Pohl, Barbara Niethammer. 2023-08-09. A Becker-D\"oring type model for cell polarization. https://doi.org/10.1007/s10955-023-03144-0

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