Large time behavior of solutions to a bipolar hydrodynamic model with big data and vacuum

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• 作者：Jing Li ; Huimin Yu ; ^{hmyu@amss.ac.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Euler&ndash ; Poisson system ; Bipolar semiconductor device ; Stationary solution ; Entropy solution ; Large time behavior
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：34
• 期：Complete
• 页码：446-458
• 全文大小：628 K

文摘

In this note, we consider a physically relevant hydrodynamic model for the bipolar semiconductor device with insulating boundary conditions and a non-flat doping profile. We prove that the corresponding steady solutions are unique and satisfy some bounded estimates, which are essential in the following consideration. For the hydrodynamic model, by means of a technical energy method and a proper entropy dissipation estimate, the large time behavior framework for any uniformly bounded weak entropy solutions with vacuum is presented. The solutions are shown to converge to the stationary solutions in L²$L^2$ norm and an exponential decay rate is also derived. No smallness and regularity conditions are assumed and the doping profile is permitted to be of big variation.