TY - JOUR
T1 - Quantum Euler-Poisson System: Local Existence of Solutions
AU - Chengchun Hao , Yueling Jia  & Hailiang Li 
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).