Nonlocal adhesion models for two cancer cell phenotypes in a multidimensional bounded domain

Cell-cell adhesion is an inherently nonlocal phenomenon. Numerous partial differential equation models with nonlocal term have been recently presented to describe this phenomenon, yet the mathematical properties of nonlocal adhesion model are not well understood. Here we consider a model with two kinds of nonlocal cell-cell adhesion, satisfying no-flux conditions in a multidimensional bounded domain. We show global-in-time well-posedness of the solution to this model and obtain the uniform boundedness of solution.

Automated summary

The study investigates a model with two types of nonlocal cell-cell adhesion, proving the global-in-time well-posedness of the solution and obtaining the uniform boundedness of the solution in a multidimensional bounded domain with no-flux conditions.