In this talk, I will present a model to describe some aspects of cell migration. Cell migration plays a key role in many physiological processes, such as embryogenesis, wound repair or metastasis formation. It is the result of a complex activity that involves different time and space scales. I will first detail the construction of the model and then present rigorous results and numerical simulations.

Keywords: complex and multiscale processes; free boundary problem; traveling-wave solution; bifurcation.