Mesenchymal motion models in one dimension

Mesenchymal motion denotes a form of cell movement through tissue which can be observed for certain cancer metastases. In [T. Hillen, J. Math. Biol., 53 (2006), pp. 585-616], a mathematical model for this form of movement was introduced. In the current paper we present a comprehensive analysis of the one-dimensional mesenchymal motion model. We establish the global existence of classical solutions and rigorously carry out the parabolic limit of the model. We discuss the stationary solutions, prove the existence of traveling wave solutions, and use numerical simulations to illustrate the results. Finally, we discuss the biological implications of the results.