主讲人:王春朋 吉林大学数学学院教授 博士生导师
时间:2019年4月19日14:00
地点:3号楼3楼332报告厅
举办单位:数理学院
主讲人介绍:吉林大学数学学院教授、博士生导师,国家自然科学基金优秀青年科学基金获得者、教育部新世纪优秀人才、吉林省长白山学者特聘教授、全国百篇优秀博士学位论文奖获得者。从事偏微分方程领域的研究,近年来围绕可压流体的跨音速流动理论,研究包含音速状态的流体流动模型以及非线性奇异偏微分方程的定性理论。多次应邀到香港中文大学、香港城市大学和意大利ICTP研究中心做学术访问。合作出版中文专著和英文专著各一部,发表学术论文近60余篇。
内容介绍:This talk concerns smooth transonic flows of Meyer type in de Laval nozzles, which are governed by an equation of mixed type with degeneracy at the sonic state. First we study the properties of sonic curves. For a C2 transonic flow of Meyer type, the set of exceptional points is shown to be a closed line segment (may be empty or only one point). The we seek smooth transonic flows of Meyer type which satisfy physical boundary conditions and whose sonic points are exceptional. For such a flow, its sonic curve must be located at the throat of the nozzle and the equation is strongly degenerate in the sense that the sonic curve is a characteristic degenerate boundary in the subsonic-sonic region, while in the sonic-supersonic region all characteristics from sonic points coincide, which are the sonic curve and never approach the supersonic region. It is proved that there exists uniquely such a smooth transonic flow near the throat of the nozzle, whose acceleration is Lipschitz continuous, if the wall of the nozzle is sufficiently flat. The global extension of this local smooth transonic flow is also studied. The works are jointed with Professor Zhouping Xin.