| Abstract: |
| Cancer growth and spread involve nonlocal phenomena, such as interactions among cells and interactions between cells and their surrounding environment. In this talk, we consider cell-cell adhesion behaviour mediated by subcellular cell-adhesion molecule binding, which plays a key role in cancer migration. Through multiscale modelling, we demonstrate that incorporating this feature leads to a system consisting of a PDE with a nonlocal spatial operator coupled with a novel nonlinear integral equation involving two nonlocal operators. The resulting system poses interesting challenges for both establishing well-posedness and numerical simulation. We establish a suitable analytical framework to prove the local well-posedness of this highly nonlocal nonlinear system in the specific case of bounded initial data with small support. |
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