On the existence of a travelling wave solution for a model of actin-based bacterial movement

Some bacteria like Listeria monocytogenes, Shigella and Rickettsia Rickettsii can move inside the host cell thanks to an actin tail. In this paper a one-dimensional model for the motion of these bacteria, introduced by B. Bazaliy, Y. Bazaliy, and A. Friedman (2007) in [2], is studied. In particular, the model is a system of partial differential equation with two moving boundaries for which we prove the existence of a travelling wave solution.