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Keywords:
quantum energy-transport model; time-discretization; periodic boundary value problem; bipolar semiconductor
quantum energy-transport model; time-discretization; periodic boundary value problem; bipolar semiconductor
Summary:
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 $\mathbb {T}^d$, the global existence of weak solutions is proved, based on a time-discretization, an entropy-type estimate, and a fixed-point argument. Furthermore, the semiclassical limit is obtained by using a priori estimates independent of the scaled Planck constant.
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