2020/10/08 by Zhigun, Anna, Surulescu, Christina · 1 citation
#35B27 35D30 35Q49 45K05 92C17 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2010.04148
In this work we upscale a prototypical kinetic transport equation which models a cell population moving in a fibrous environment with a chemo- or haptotactic signal influencing both the direction and the magnitude of the cell velocity. The presented approach to scaling does not rely on orthogonality and treats parabolic and hyperbolic scalings in a unified manner. It is shown that the steps of the formal limit procedures are mirrored by rigorous operations with finite measures provided that the measure-valued position-direction fiber distribution enjoys some spacial continuity.