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Record Nr. |
UNISA996466400403316 |
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Autore |
Buttenschön Andreas |
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Titolo |
Non-local cell adhesion models : symmetries and bifurcations in 1-D / / Andreas Buttenschön, Thomas Hillen |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2021] |
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©2021 |
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ISBN |
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Edizione |
[1st ed. 2021.] |
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Descrizione fisica |
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1 online resource (VIII, 152 p. 35 illus., 15 illus. in color.) |
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Collana |
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CMS/CAIMS Books in Mathematics |
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Disciplina |
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Soggetti |
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Cell adhesion - Mathematical models |
Interacció cel·lular |
Models matemàtics |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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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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Sommario/riassunto |
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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. |
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