ALGEBRAIC TIME DECAY FOR THE BIPOLAR QUANTUM HYDRODYNAMIC MODEL

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 ...

The Quantum Hydrodynamic Model for Semiconductor Devices

ar X iv : 0 81 1 . 37 90 v 1 [ m at h - ph ] 2 4 N ov 2 00 8 Algebraic time - decay for the bipolar quantum hydrodynamic model ∗

The initial value problem is considered in the present paper for bipolar quantum hydrodynamic model for semiconductors (QHD) in R. We prove that the unique strong solution exists globally in time and tends to the asymptotical state with an algebraic rate as t → +∞. And, we show that the global solution of linearized bipolar QHD system decays in time at an algebraic decay rate from both above an...

Exponential decay in time of solutions of the viscous quantum hydrodynamic equations

The long-time asymptotics of solutions of the viscous quantum hydrodynamic model in one space dimension is studied. This model consists of continuity equations for the particle density and the current density, coupled to the Poisson equation for the electrostatic potential. The equations are a dispersive and viscous regularization of the Euler equations. It is shown that the solutions converge ...

N ov 2 00 8 Semiclassical and relaxation limits of bipolar quantum hydrodynamic model ∗

The global in-time semiclassical and relaxation limits of the bipolar quantum hydrodynamic model for semiconductors are investigated in R. We prove that the unique strong solution converges globally in time to the strong solution of classical bipolar hydrodynamical equation in the process of semiclassical limit and to that of the classical Drift-Diffusion system under the combined relaxation an...