主讲人：王春朋 吉林大学数学学院教授 博士生导师
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.