文献类型：期刊文献

中文题名：Asymptotic Behavior of Solutions of the Bipolar Quantum Drift-Diffusion Model in the Quarter Plane

英文题名：Asymptotic Behavior of Solutions of the Bipolar Quantum Drift-Diffusion Model in the Quarter Plane

作者：LIU fang[1];LI Yeping[1]

机构：[1]Department of Mathematics, East China University of Science and Technology

年份：2019

卷号：24

期号：6

起止页码：467

中文期刊名：Wuhan University Journal of Natural Sciences

外文期刊名：武汉大学学报（自然科学英文版）

收录：CSTPCD;;Scopus;CSCD:【CSCD2019_2020】；

基金：Supported by the National Natural Science Foundation of China(11671134)

语种：英文

中文关键词：asymptotic;behavior;quantum;drift-diffusion;model;self-similar;wave;energy;estimate

外文关键词：asymptotic behavior;quantum drift-diffusion model;self-similar wave;energy estimate

摘要：In this study, we consider the one-dimensional bipolar quantum drift-diffusion model, which consists of the coupled nonlinear fourth-order parabolic equation and the electric field equation. We first show the global existence of the strong solution of the initial boundary value problem in the quarter plane. Moreover, we show the self-similarity property of the strong solution of the bipolar quantum drift-diffusion model in the large time. Namely, we show the unique global strong solution with strictly positive density to the initial boundary value problem of the quantum drift-diffusion model, which in large time, tends to have a self-similar wave at an algebraic time-decay rate. We prove them in an energy method.
In this study, we consider the one-dimensional bipolar quantum drift-diffusion model, which consists of the coupled nonlinear fourth-order parabolic equation and the electric field equation. We first show the global existence of the strong solution of the initial boundary value problem in the quarter plane. Moreover, we show the self-similarity property of the strong solution of the bipolar quantum drift-diffusion model in the large time. Namely, we show the unique global strong solution with strictly positive density to the initial boundary value problem of the quantum drift-diffusion model, which in large time, tends to have a self-similar wave at an algebraic time-decay rate. We prove them in an energy method.