Acta mathematica scientia,Series B

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LARGE-TIME BEHAVIOR OF SOLUTIONS OF QUANTUM HYDRODYNAMIC MODEL FOR SEMICONDUCTORS

Jia Yueling; Li Hailiang   

  1. LCP, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China
  • Received:2003-08-04 Revised:1900-01-01 Online:2006-01-20 Published:2006-01-20
  • Contact: Jia Yueling

Abstract:

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 the steady-state solution, is obtained. This solution tends to the corresponding steady-state solution exponentially fast as the time tends to infinity.

Key words: Quantum hydrodynamic equation, quantum Euler-Poisson system, global existence of classical solution, nonlinear fourth-order wave equation,
exponential decay,
large-time behavior

CLC Number: 

  • 35J40
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