CSDC Seminar: Nonlocal advection-diffusion model in cancer invasion

Cancer growth and spread involve nonlocal phenomena, such as interactions between cells and their surrounding environment. Cells bind to neighbouring cells and the extracellular matrix through cell-adhesion molecule (CAM) bindings. These bindings play a key role in cancer cell migration and invasion.

Through multiscale modelling, it is demonstrated that incorporating these characteristics leads to a diffusion-advection equation with a nonlocal operator in space, coupled with a novel nonlinear integral equation with two nonlocal operators. These nonlocalities present interesting challenges in establishing the well-posedness of the system and in performing numerical simulations.