Quasi-Neutral Limit to Steady-State Hydrodynamic Model of Semiconductors with Degenerate Boundary.

This paper is concerned with the quasi-neutral limit to a one-dimensional steady hydrodynamic model of semiconductors in the form of Euler-Poisson equations with degenerate boundary, a difficult case caused by the boundary layers and degeneracy. We establish a so-called convexity structure of the sequence of subsonic-sonic solutions near the boundary domains in this limit process, which efficiently overcomes the degenerate effect. We first show the strong convergence in the L2 norm with the order O(\lambda; ) for the Debye length \lambda when the doping profile is continuous. Then we derive the uniform error estimates in the L\infty norm with the order O(\lambda) when the doping profile has higher regularity. The proof of L\infty boundedness is based on a new bounded estimate method, which is used to replace the maximum principle utilized in the nondegenerate case. These newly proposed techniques in asymptotic limit analysis develop and improve the existing studies.