# Nonlocal Adhesion Models for Microorganisms on Bounded Domains

## TL;DR

This paper develops and analyzes nonlocal adhesion models for microorganisms on bounded domains, proving existence and uniqueness, and demonstrating boundary behavior and pattern formation through numerical simulations.

## Contribution

It introduces boundary conditions for 1D nonlocal adhesion models, proves mathematical well-posedness, and explores boundary effects and pattern formation numerically.

## Key findings

- Solutions exhibit known fluid adhesion behavior
- Interior pattern formation observed
- Boundary conditions influence solution dynamics

## Abstract

In 2006 Armstrong, Painter and Sherratt formulated a non-local differential equation model for cell-cell adhesion. For the one dimensional case we derive various types of adhesive, repulsive, and no-flux boundary bonditions. We prove local and global existence and uniqueness for the resulting integro-differential 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.