In this paper, we construct a model to describe the spatial motion of a monolayer of cells occupying a two-dimensional dish. By taking care of nonlocal contact inhibition, quiescence phenomenon, and the cell cycle, we derive porous media-like equation with nonlocal reaction terms. The first part of this paper is devoted to the construction of the model. In the second part we study the well-posedness of the model. We conclude the paper by presenting some numerical simulations of the model and we observe the formation of colonies.
|Number of pages||22|
|Journal||Mathematical Models and Methods in Applied Sciences|
|Issue number||SUPPL. 1|
|Publication status||Published - Apr 2011|
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Applied Mathematics