  We examine 2D electron transport through a long narrow channel driven by an
external electric field in presence of diffusive boundary scattering. At zero
temperature, we derive an analytical solution of the transition from ballistic
to diffusive transport if we increase the bulk disorder strength. This
crossover yields characteristic current density profiles. Furthermore, we
illustrate the current density in the transition from ballistic to hydrodynamic
transport. This corresponds to the Gurzhi effect in the resistivity. We also
study the influence of finite temperature on current densities and average
current in this system. In particular, we analyze how different scaling laws of
scattering with respect to temperature affect the current profile along the
channel.
