  A one-dimensional cross-diffusion system modeling the transport of vesicles
in neurites is analyzed. The equations are coupled via nonlinear Robin boundary
conditions to ordinary differential equations for the number of vesicles in the
reservoirs in the cell body and the growth cone at the end of the neurite. The
existence of bounded weak solutions is proved by using the
boundedness-by-entropy method. Numerical simulations show the dynamical
behavior of the concentrations of anterograde and retrograde vesicles in the
neurite.
