KMS Of Academy of mathematics and systems sciences, CAS
| Existence and stability of steady-state of one-dimensional quantum hydrodynamic system for semiconductors | |
Huang, Feimin ; Li, Hai-Liang; Matsumura, Akitaka
| |
| 2006-06-01 | |
| Source Publication | JOURNAL OF DIFFERENTIAL EQUATIONS
 |
| ISSN | 0022-0396 |
| Volume | 225Issue:1Pages:1-25 |
| Abstract | A transient quantum hydrodynamic system for charge density, current density and electrostatic potential is considered in spatial one-dimensional real line. The equations take the form of classical Euler-Poisson system with additional dispersion caused by the quantum (Bohm) potential and used, for instance, to account for quantum mechanical effects in the modelling of charge transport in ultra submicron semiconductor devices such as resonant tunnelling trough oxides gate and inversion layer energy quantization and so on. The existence and uniqueness and long time stability of steady-state solution with spatial different end states and large strength is proven in Sobolev space. To guarantee the existence and stability, we propose a stability condition which can be viewed as a quantum correction to classical subsonic condition. Furthermore. since the argument for classical hydrodynamic equations does not apply here due to the dispersion term. we also show the local-in-time existence of strong solution in terms of a reformulated system for the charge density and the electric field consisting of two coupled semilinear (spatial) fourth-order wave type equations. (c) 2006 Elsevier Inc. All rights reserved. |
| Keyword | quantum hydrodynamic models existence and exponential stability of steady-state global existence of smooth solutions semiconductor model |
| DOI | 10.1016/j.jde.2006.02.002 |
| Language | 英语 |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics |
| WOS ID | WOS:000238045600001 |
| Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/2801 |
| Collection | 应用数学研究所 |
| Corresponding Author | Huang, Feimin |
| Affiliation | 1.Acad Sinica, Inst Appl Math, AMSS, Beijing 100080, Peoples R China 2.Capital Normal Univ, Dept Math, Beijing 100037, Peoples R China 3.Osaka Univ, Dept Pure & Appl Math, Grad Sch Informat Sci & Technol, Toyonaka, Osaka 5600043, Japan |
| Recommended Citation GB/T 7714 | Huang, Feimin,Li, Hai-Liang,Matsumura, Akitaka. Existence and stability of steady-state of one-dimensional quantum hydrodynamic system for semiconductors[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2006,225(1):1-25. |
| APA | Huang, Feimin,Li, Hai-Liang,&Matsumura, Akitaka.(2006).Existence and stability of steady-state of one-dimensional quantum hydrodynamic system for semiconductors.JOURNAL OF DIFFERENTIAL EQUATIONS,225(1),1-25. |
| MLA | Huang, Feimin,et al."Existence and stability of steady-state of one-dimensional quantum hydrodynamic system for semiconductors".JOURNAL OF DIFFERENTIAL EQUATIONS 225.1(2006):1-25. |
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