Non-Local Cell Adhesion Models: Symmetries and Bifurcations in 1-D

Main subject categories: • Differential equations • Mathematical biology • Mathematical modelling of biologic processes • Cell adhesion

Mathematics Subject Classification: • 35R09 Integro-partial differential equations • 45K05 Integro-partial differential equations • 35Q92 Integro-partial differential equations • 92C15 Developmental biology, pattern formation • 47G20 Integro-differential operators

This monograph considers the mathematical modeling of cellular adhesion, a key interaction force in cell biology. While deeply grounded in the biological application of cell adhesion and tissue formation, this monograph focuses on the mathematical analysis of non-local adhesion models. The novel aspect is the non-local term (an integral operator), which accounts for forces generated by long ranged cell interactions. The analysis of non-local models has started only recently, and it has become a vibrant area of applied mathematics. This monograph contributes a systematic analysis of steady states and their bifurcation structure, combining global bifurcation results pioneered by Rabinowitz, equivariant bifurcation theory, and the symmetries of the non-local term. These methods allow readers to analyze and understand cell adhesion on a deep level.

pdf and epub included in zip file.