Global solutions to isothermal system in a divergent nozzle with friction

In this paper, we remove the restriction A′(x)≥0 in the paper 'Lu (2011)', the restriction z0(x)≤0 or w0(x)≤0 in the paper 'Klingenberg and Lu (1997)', and obtain the global existence of entropy solutions to the isothermal gas dynamics system in a divergent nozzle with friction.