Semiclassical limit of a simplified quantum energy-transport model for bipolar semiconductors

Sungjin Ra; Choljin Jang; Jinmyong Hong

Applications of Mathematics (2024)

  • Volume: 69, Issue: 4, page 513-540
  • ISSN: 0862-7940

Abstract

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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 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.

How to cite

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Ra, Sungjin, Jang, Choljin, and Hong, Jinmyong. "Semiclassical limit of a simplified quantum energy-transport model for bipolar semiconductors." Applications of Mathematics 69.4 (2024): 513-540. <http://eudml.org/doc/299494>.

@article{Ra2024,
abstract = {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.},
author = {Ra, Sungjin, Jang, Choljin, Hong, Jinmyong},
journal = {Applications of Mathematics},
keywords = {quantum energy-transport model; time-discretization; periodic boundary value problem; bipolar semiconductor},
language = {eng},
number = {4},
pages = {513-540},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Semiclassical limit of a simplified quantum energy-transport model for bipolar semiconductors},
url = {http://eudml.org/doc/299494},
volume = {69},
year = {2024},
}

TY - JOUR
AU - Ra, Sungjin
AU - Jang, Choljin
AU - Hong, Jinmyong
TI - Semiclassical limit of a simplified quantum energy-transport model for bipolar semiconductors
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 4
SP - 513
EP - 540
AB - 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.
LA - eng
KW - quantum energy-transport model; time-discretization; periodic boundary value problem; bipolar semiconductor
UR - http://eudml.org/doc/299494
ER -

References

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