Hirvonen, P. (2024). Analysis of a Poisson-Nernst-Planck System with Steric Effect. In Complexity of Life Conference: Bridging complexity scales and biological systems (pp. 39–39).
This talk presents an analysis of a modified Poisson-Nernst-Planck system with so-called steric effect for an arbitrary number of species, modeling ion transport in a small domain. The additional term appearing in the equations was suggested by Lin and Eisenberg, aiming to include ion sizes, which are not taken into account in the original Poisson-Nernst-Planck equations. The focus of this talk lies in the mathematical treatment of the equations, proving global existence of weak solutions using the boundedness-by-entropy method, as well as the weak-strong uniqueness property, which is shown by means of a relative entropy inequality. Moreover, other topics, such as the boundedness of weak solutions and long-time behaviour are discussed.
