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

Mengmeng Shang

doi:10.3934/math.2017.1.102

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 solutions converge to the stationary solutions in $L^2$ norm with exponential decay rate. No regularity and smallness conditions are assumed.

Highlights

In this paper, isentropic Euler-Poisson equations for the bipolar hydrodynamic model of semiconductor devices are considered
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 solutions converge to the stationary solutions in L2 norm with exponential decay rate

Summary

Introduction

Isentropic Euler-Poisson equations for the bipolar hydrodynamic model of semiconductor devices are considered. With the smallness assumption on the amplitude of background electron current, [1] first proved the uniformly bounded density weak entropy solutions of the unipolar hydrodynamic model (1.5), decay exponentially to the stationary solutions. Instead of proving the hard bone (1.6), we will give a large time behavior framework for density time-increasing entropy solutions to the bipolar hydrodynamic model (1.1) − (1.3). The vector function (n1, n2, J1, J2, E) is a weak solution of problem (1.1) − (1.4), if it satisfies the equation (1.1) in the distributional sense, verifies the restriction (1.3) and (1.4).

AIMS Mathematics

Large time behavior framework of time-increasing entropy solutions