Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 80, Issue 1, Pages 382-401Publisher
SIAM PUBLICATIONS
DOI: 10.1137/19M1250315
Keywords
cell-cell adhesion; nonlocal models; no-flux boundary conditions; global existence; semigroups
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Funding
- NSERC
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In 2006 Armstrong, Painter, and Sherratt formulated a nonlocal differential equation model for cell-cell adhesion. For the one-dimensional case on a bounded domain we derive various types of biological boundary conditions, describing adhesive, repulsive, and neutral boundaries. We prove local and global existence and uniqueness for the resulting integrodifferential equations. In numerical simulations we consider adhesive, repulsive, and neutral boundary conditions, and we show that the solutions mimic known behavior of fluid adhesion to boundaries. In addition, we observe interior pattern formation due to cell-cell adhesion.
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