Article
| Title: | Semiclassical limit of a simplified quantum energy-transport model for bipolar semiconductors (English) |
| Author: | Ra, Sungjin |
| Author: | Jang, Choljin |
| Author: | Hong, Jinmyong |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 69 |
| Issue: | 4 |
| Year: | 2024 |
| Pages: | 513-540 |
| Summary lang: | English |
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| Category: | math |
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| 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. (English) |
| Keyword: | quantum energy-transport model |
| Keyword: | time-discretization |
| Keyword: | periodic boundary value problem |
| Keyword: | bipolar semiconductor |
| MSC: | 35K20 |
| MSC: | 82D37 |
| DOI: | 10.21136/AM.2024.0016-24 |
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| Date available: | 2024-08-27T11:19:51Z |
| Last updated: | 2024-09-02 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152532 |
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