Relaxation-time limits of non-isentropic hydrodynamic models for semiconductors

The Relaxation-Time Limit in the Quantum Hydrodynamic Equations for Semiconductors

The relaxation-time limit from the quantum hydrodynamic model to the quantum drift-diffusion equations in R3 is shown for solutions which are small perturbations of the steady state. The quantum hydrodynamic equations consist of the isentropic Euler equations for the particle density and current density including the quantum Bohm potential and a momentum relaxation term. The momentum equation i...

Large Time Behavior of Solutions to n-Dimensional Bipolar Hydrodynamic Models for Semiconductors

Abstract. In this paper, we study the n-dimensional (n ≥ 1) bipolar hydrodynamic model for semiconductors in the form of Euler-Poisson equations. In 1-D case, when the difference between the initial electron mass and the initial hole mass is non-zero (switch-on case), the stability of nonlinear diffusion wave has been open for a long time. In order to overcome this difficulty, we ingeniously co...

Zero–Relaxation–Time Limits in the Hydrodynamic Equations for Plasmas Revisited

A rigorous proof of the zero-relaxation-time limits in the hydrodynamic equations for plasmas is given. The equations consist of the Euler equations for the electrons and/or ions coupled with a linear or nonlinear Poisson equation. The proof is based on high energy estimates for the Euler equations and appropriate compactness arguments. The theorem is valid for all adiabatic states for both ele...

Zero-Mass-Electrons Limits in Hydrodynamic Models for Plasmas

Large time behavior framework for the time-increasing weak solutions of bipolar hydrodynamic model of semiconductors

Abstract: In this paper, we consider an isentropic Euler-Poisson equations for the bipolar hydrodynamic model of semiconductor devices, which has a non-flat doping profile and insulating boundary conditions. Using a technical energy method and an entropy dissipation estimate, we present a framework for the large time behavior of time-increasing weak entropy solutions. It is shown that the weak ...