Semiclassical limit of a simplified quantum energy-transport model for bipolar semiconductors
We are concerned with a simplified quantum energy-transport model for bipolar semiconductors, which consists of nonlinear parabolic fourth-order equations for the electron and hole density; degenerate elliptic heat equations for the electron and hole temperature; and Poisson equation for the electric potential. For the periodic boundary value problem in the torus , the global existence of weak solutions is proved, based on a time-discretization, an entropy-type estimate, and a fixed-point argument....