Details

Non-Local Cell Adhesion Models

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

von: Andreas Buttenschön, Thomas Hillen
90,94 €
Verlag:	Springer
Format:	PDF
Veröffentl.:	09.06.2021
ISBN/EAN:	9783030671112
Sprache:	englisch

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Beschreibungen

Titelbeschreibung

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.

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.

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Sonderbeitrag

Presents the first ever application of abstract bifurcation theory to a non-local problem Includes leading research on pattern formation of non-local models Describes in detail the development of basic properties of nonlocal adhesion models Defines biological non-local boundary conditions