The existence of global weak solutions is shown for the equations of isentropic gas dynamics with inhomogeneous terms by the viscosity method. A generalised version of the method of invariant regions is developed to obtain the uniform L∞ bounds of the viscosity solutions, and the method of compensated compactness is applied to show the existence of weak solutions as limits of the viscosity solutions. The lower positive bound for the density function is also obtained. As an example, a hydrodynamic model for semiconductors is analysed.