Relaxation-time limits of global solutions in full quantum hydrodynamic model for semiconductors
This paper is concerned with the global well-posedness and relaxation-time limits for the solutions in the full quantum hydrodynamic model, which can be used to analyze the thermal and quantum influences on the transport of carriers in semiconductor devices. For the Cauchy problem in , we prove the global existence, uniqueness and exponential decay estimate of smooth solutions, when the initial data are small perturbations of an equilibrium state. Moreover, we show that the solutions converge into...