Non-local cell adhesion models : symmetries and bifurcations in 1-D / Andreas Buttenschön, Thomas Hillen.

Format:

Book

Author/Creator:

Buttenschön, Andreas, author.

Hillen, Thomas, author.

Series:

CMS/CAIMS books in mathematics.

CMS/CAIMS Books in Mathematics

Language:

English

Subjects (All):

Cell adhesion--Mathematical models.

Cell adhesion.

Physical Description:

1 online resource (VIII, 152 p. 35 illus., 15 illus. in color.)

Edition:

1st ed. 2021.

Place of Publication:

Cham, Switzerland : Springer, [2021]

Summary:

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.

Contents:

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.

Notes:

Description based on print version record.

ISBN:

3-030-67111-9

OCLC:

1256541830