Format:
1 Online-Ressource (VIII, 152 Seiten)
ISBN:
9783030671112
Series Statement:
CMS/CAIMS books in mathematics
Content:
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.
Note:
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.
Additional Edition:
ISBN 9783030671105
Additional Edition:
ISBN 9783030671129
Additional Edition:
ISBN 9783030671136
Language:
English
Keywords:
Zelladhäsion
;
Mathematisches Modell
;
Integrodifferentialgleichung
;
Nichtlokalität
;
Verzweigung
;
Randwertproblem
DOI:
10.1007/978-3-030-67111-2
