Quasineutral limit of bipolar quantum hydrodynamic model for semiconductors

Abstract

This paper is concerned with the quasineutral limit of the bipolar quantum hydrodynamic model for semiconductors. It is rigorously proved that the strong solutions of the bipolar quantum hydrodynamic model converge to the strong solution of the so-called quantum hydrodynamic equations as the Debye length goes to zero. Moreover, we obtain the convergence of the strong solutions of bipolar quantum hydrodynamic model to the strong solution of the compressible Euler equations with damping if both the Debye length and the Planck constant go to zero simultaneously.Keywords Bipolar quantum hydrodynamic model, quantum hydrodynamic equations, compressible Euler equations, quasineutral limit, modulated energy functional MSC 76Y05, 82D37, 82D10