CMS/CAIMS Books in Mathematics: Symmetries and Bifurcations in 1-D

Buttenschön, Andreas; Hillen, Thomas

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.

Details

Published by: Springer

Publication Date: 2021-06-10

Format: Hardcover

ISBN-13: 9783030671105

DOI: 10.1007/978-3-030-67111-2

Dimensions: 235cm x155cm

Pages: 152