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