摘要
A one-dimensional quantum hydrodynamic model （or quantum Euler-Poisson system） for semiconductors with initial boundary conditions is considered for general pressure-density function. The existence and uniqueness of the classical solution of the corresponding steady-state quantum hydrodynamic equations is proved. Furthermore, the global existence of classical solution, when the initial datum is a perturbation of t he steadystate solution, is obtained. This solution tends to the corresponding steady-state solution exponentially fast as the time tends to infinity.
A one-dimensional quantum hydrodynamic model （or quantum Euler-Poisson system） for semiconductors with initial boundary conditions is considered for general pressure-density function. The existence and uniqueness of the classical solution of the corresponding steady-state quantum hydrodynamic equations is proved. Furthermore, the global existence of classical solution, when the initial datum is a perturbation of t he steadystate solution, is obtained. This solution tends to the corresponding steady-state solution exponentially fast as the time tends to infinity.
基金
The first author was supported by the China Postdoctoral Science Foundation(2005037318)The second author acknowledges partial support from the Austrian-Chinese Scientific-Technical Collaboration Agreement, the CTS of Taiwanthe Wittgenstein Award 2000 of P.A. Markowich, funded by the Austrian FWF, the Grants-in-Aid of JSPS No.14-02036the NSFC(10431060)the Project-sponsored by SRF for ROCS, SEM
