3522vip浦京集团官网2023年第15期数理大讲堂

暨“喜迎90周年校庆”系列讲座第30期

报告人：孙文龙长江大学副教授，硕士生导师（3522vip浦京集团官网校友）

报告时间：2023年5月26日上午10：30—11：30

地点：3522vip浦京集团官网3号楼3B205

主持人：赵才地教授

报告题目：The full viscous quantum hydrodynamic system in one dimensional space

报告摘要：A viscous quantum hydrodynamic system for particle density, current density, energy density and electrostatic potential, coupled with a Poisson equation, is studied in spatial one dimensional real line. The system is self-consistent in the sense that the electric field, which forms a forcing term in the momentum and energy equations, is determined by the coupled Poisson equation. First the existence and uniqueness of the stationary solution is proved in an appropriate Sobolev space. Then exponential stability of the stationary solution is established by constructing an apriori estimate. Since the techniques for classical hydrodynamic equations are not applicable here due to the quantum term, the existence of a local-in-time solution is obtained by showing the existence of local-in-time solutions of a reformulated system via the iteration method.

报告人简介：孙文龙，博士，长江大学副教授，硕士生导师。研究方向为无穷维动力系统与非线性偏微分方程，曾在美国奥拉巴马大学学术访问一年，在《J. Math. Phys》、《Topol. Method nonlinear Anal.》、《Comm. Math. Sci.》、《Dynamics of PDE》、《Discrete Cont. Dyn. Syst. Ser. B》等期刊上发表学术论文十余篇。