Volume 16, Issue 4
Quantum Euler-Poisson System: Local Existence of Solutions

Chengchun Hao , Yueling Jia & Hailiang Li

DOI:

J. Part. Diff. Eq., 16 (2003), pp. 306-320.

Published online: 2003-11

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  • Abstract

The one-dimensional transient quantum Euler-Poisson system for semiconductors is studied in a bounded interval. The quantum correction can be interpreted as a dispersive regularization of the classical hydrodynamic equations and mechanical effects. The existence and uniqueness of local-in-time solutions are proved with lower regularity and without the restriction on the smallness of velocity, where the pressure-density is general (can be non-convex or non-monotone).

  • Keywords

Quantum Euler-Poisson system existence of local classical solutions non-linear fourth-order wave equation

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@Article{JPDE-16-306, author = {}, title = {Quantum Euler-Poisson System: Local Existence of Solutions}, journal = {Journal of Partial Differential Equations}, year = {2003}, volume = {16}, number = {4}, pages = {306--320}, abstract = { The one-dimensional transient quantum Euler-Poisson system for semiconductors is studied in a bounded interval. The quantum correction can be interpreted as a dispersive regularization of the classical hydrodynamic equations and mechanical effects. The existence and uniqueness of local-in-time solutions are proved with lower regularity and without the restriction on the smallness of velocity, where the pressure-density is general (can be non-convex or non-monotone).}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5428.html} }
TY - JOUR T1 - Quantum Euler-Poisson System: Local Existence of Solutions JO - Journal of Partial Differential Equations VL - 4 SP - 306 EP - 320 PY - 2003 DA - 2003/11 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5428.html KW - Quantum Euler-Poisson system KW - existence of local classical solutions KW - non-linear fourth-order wave equation AB - The one-dimensional transient quantum Euler-Poisson system for semiconductors is studied in a bounded interval. The quantum correction can be interpreted as a dispersive regularization of the classical hydrodynamic equations and mechanical effects. The existence and uniqueness of local-in-time solutions are proved with lower regularity and without the restriction on the smallness of velocity, where the pressure-density is general (can be non-convex or non-monotone).
Chengchun Hao , Yueling Jia & Hailiang Li . (2019). Quantum Euler-Poisson System: Local Existence of Solutions. Journal of Partial Differential Equations. 16 (4). 306-320. doi:
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