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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.
Table des matières
Introduction.- Preliminaries.- The Periodic Problem.- Basic Properties.- Local Bifurcation.- Global Bifurcation.- Non-local Equations with Boundary Conditions.- No-flux Boundary Conditions.- Discussion and future directions.
Commentaire
"Modelers who wish to use similar approaches in their modeling will find this a good source of base information, as well as a valuable guide for initiating similar analyses for their own models. Analysts wishing to expand our understanding ... will find this book a fine building block. It could also prove a useful resource for graduate students looking for potential projects ... . this monograph is an admirable attempt ... and hopefully will inspire significant further study." (Kevin Painter, SIAM Review, Vol. 64 (1), March, 2022)
"The detailed analysis, as presented here, shows a stimulating interaction between model symmetries, mathematical analysis, and biological reality, which probably are inspired the authors and hopefully the readers of this book too." (Andrey Zahariev, zbMATH 1473.92001, 2021)
