Weak solutions to isothermal hydrodynamic model for semiconductor devices

In this paper, the Cauchy problem of the isothermal hydrodynamic model for semiconductor devices is investigated. The existence of global weak entropy solutions with large initial data is obtained by using a modified fractional step Lax-Friedrichs scheme and the theory of compensated compactness. As a byproduct, the existence of entropy solutions to the Cauchy problem of the isentropic hydrodynamic model for a semiconductor with infinite mass is also proved.