EXISTENCE AND UNIQUENESS FOR A STATIONARY HYBRID QUANTUM HYDRODYNAMICAL MODEL WITH GENERAL PRESSURE FUNCTIONAL*

In this paper we generalize the results obtained in [F. Di Michele, M. Mei, B. Rubino, and R. Sampalmieri, Int. J. Numer. Anal. Model., 13:898–925, 2016], where a hybrid model for semiconductor devices has been presented. In particular we consider a more general pressure function, which allows us to account also for the isotropic case. General Dirichlet boundary conditions are also included. In this case we need a different and more restrictive subsonic condition which directly involves the first derivative of the quantum function Q(x). The existence of solutions is obtained by regularizing the problem and performing a suitable vanishing viscosity limit. Also the zero-charge-space limit is discussed and our results are tested on a simple toy model.