Non-Local Cell Adhesion Models: Symmetries and Bifurcations in 1-D, Paperback/Andreas Buttenschön

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. 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. Book specifications: Collection: Cms/Caims Books in Mathematics Dimensions: 234 x 156 Author: Andreas Buttenschön Cover type: Paperback Publishing Year: 2022 Publishing Month: 6 Pages: 152 Language: English Publisher: Springer Weight: 236 g