Buttenschön / Hillen Non-Local Cell Adhesion Models

Symmetries and Bifurcations in 1-D
1. Auflage 2021
ISBN: 978-3-030-67111-2
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 1, 152 Seiten, eBook

Reihe: CMS/CAIMS Books in Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Buttenschön, Andreas

Hillen, Thomas

Inhaltsverzeichnis

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.