Abstract
Tumour invasion is an essential stage of cancer progression. Its main drivers are diffusion and taxis, a directed movement along the gradient of a stimulus. Here we review models with flux limited diffusion and/or taxis which have applications in modelling of cell migration, particularly in cancer. Flux limitation ensures control upon propagation speeds, precluding unnaturally quick spread which is typical for traditional parabolic equations. We recall the main properties of models with flux limitation effects and discuss ways to construct them, concentrating on multiscale derivations from kinetic transport equations.
| Original language | English |
|---|---|
| Pages (from-to) | 5-26 |
| Journal | Mathematical Proceedings of the Royal Irish Academy |
| Volume | 122A |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 30 Mar 2022 |
Bibliographical note
Review articleKeywords
- math.AP
- 35K55 35K65 35Q49 35Q83 35Q92 45K05 92C17
Access to Document
- Flux limitation mechanisms arising in multiscale modelling of cancer invasion
Copyright 2022 the authors. This is an open access article published under a Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.