Geodesic
Semiclassical limit of a simplified quantum energy-transport model for bipolar semiconductors
Applications of Mathematics, Tome 69 (2024) no. 4, pp. 513-540 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/AM.2024.0016-24
Classification : 35K20, 82D37
Keywords: quantum energy-transport model; time-discretization; periodic boundary value problem; bipolar semiconductor 
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Ra, Sungjin; Jang, Choljin; Hong, Jinmyong. Semiclassical limit of a simplified quantum energy-transport model for bipolar semiconductors. Applications of Mathematics, Tome 69 (2024) no. 4, pp. 513-540. doi: 10.21136/AM.2024.0016-24

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