LARGE-TIME BEHAVIOR OF SOLUTIONS OF QUANTUM HYDRODYNAMIC MODEL FOR SEMICONDUCTORS1

  • Jia Y
  • Li H
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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. © 2006 Wuhan Institute of Physics and Mathematics.

Author-supplied keywords

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

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Authors

  • Yueling Jia

  • Hailiang Li

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