AIMS Mathematics, 2017, 2(1): 102-110. doi: 10.3934/Math.2017.1.102

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

Department of Mathematics, Shandong Normal University, Jinan, 250014, China

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.
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Keywords Euler-Poisson system; bipolar semiconductor device; entropy solution; stationary solution; large time behavior

Citation: Mengmeng Shang. Large time behavior framework for the time-increasing weak solutions of bipolar hydrodynamic model of semiconductors. AIMS Mathematics, 2017, 2(1): 102-110. doi: 10.3934/Math.2017.1.102


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