Del 1 - CMS/CAIMS Books in Mathematics

Non-Local Cell Adhesion Models

Symmetries and Bifurcations in 1-D

Häftad, Engelska, 2022

Av Andreas Buttenschön, Thomas Hillen, Andreas Buttenschon

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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.

Produktinformation

Utgivningsdatum2022-06-11
Mått155 x 235 x 15 mm
Vikt256 g
FormatHäftad
SpråkEngelska
SerieCMS/CAIMS Books in Mathematics
Antal sidor152
FörlagSpringer Nature Switzerland AG
ISBN9783030671136

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“Modelers who wish to use similar approaches in their modeling will find this a good source of base information, as well as a valuable guide for initiating similar analyses for their own models. Analysts wishing to expand our understanding … will find this book a fine building block. It could also prove a useful resource for graduate students looking for potential projects … . this monograph is an admirable attempt … and hopefully will inspire significant further study.” (Kevin Painter, SIAM Review, Vol. 64 (1), March, 2022)“The detailed analysis, as presented here, shows a stimulating interaction between model symmetries, mathematical analysis, and biological reality, which probably are inspired the authors and hopefully the readers of this book too.” (Andrey Zahariev, zbMATH 1473.92001, 2021)