Partial Differential Equation Models of Active Transport in Neuronal Axons

Abstract

The purpose of this thesis is to perform some mathematical analysis and study numerical solutions of different models describing (different aspects of) axonal transport. We will explain our numerical results using mathematical analysis and our intuitive understanding of the equations in the different models. We will also derive some mathematical results (e.g. a uniqueness and existence result and discrete maximum principles) which will shed light on the understanding of the models, both analytically and numerically.