Asymptotic Behavior of Solutions of the Bipolar Quantum Drift-Diffusion Model in the Quarter Plane  

作　　者：LIU fang LI Yeping 

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

出　　处：《Wuhan University Journal of Natural Sciences》2019年第6期467-473,共7页武汉大学学报（自然科学英文版）

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

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.

关 键 词：ASYMPTOTIC behavior quantum DRIFT-DIFFUSION model SELF-SIMILAR wave energy ESTIMATE 

分 类 号：O175.2[理学—数学]