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＜E-Book＞
Non-Local Cell Adhesion Models : Symmetries and Bifurcations in 1-D / by Andreas Buttenschön, Thomas Hillen
(CMS/CAIMS Books in Mathematics. ISSN:27306518 ; 1)

Edition	1st ed. 2021.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2021
Language	English
Size	VIII, 152 p. 35 illus., 15 illus. in color : online resource
Authors	*Buttenschön, Andreas author Hillen, Thomas author SpringerLink (Online service)
Subjects	LCSH:Biomathematics LCSH:Mathematical models FREE:Mathematical and Computational Biology FREE:Mathematical Modeling and Industrial Mathematics
Notes	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 HTTP:URL=https://doi.org/10.1007/978-3-030-67111-2

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