学术报告报告题目1：LifeSpan for a Semilinear Heat Equation with Initial Data non Rarefied
at$\infty$
报告人：尹景学教授（华南师范大学，长江学者特聘教授，国家杰出青年基金获得者）
报告时间：2015年11月13日上午9:00-10:30
报告题目2：SmoothTransonic Flows of Meyer Type in De Laval Nozzles
报告人：王春朋教授（吉林大学）
报告时间：2015年11月13日上午10:30-12:00
报告地点：4号楼4318室
欢迎广大师生参加。
数学学院
2015年11月12日
报告1摘要：Inthis talk, we discuss the life span of solutions for the heatequation with nonlinear sources. We will show that as long as theinitial datum is non-rarefied at $\infinity$, the solution must blowup at finite time.Moreover, we give an delicate estimate on the lifespan.
报告2摘要：Thistalk concerns smooth transonic steady potential flows of Meyer typein two-dimensional de Laval nozzles, which are governed by anequation of mixed type with degeneracy at the sonic state. For a$C^2$ transonic flow of Meyer type, it is shown that the set ofexceptional points is a closed line segment (may be empty or only onepoint). Furthermore, a smooth transonic flow of Meyer type withnonexceptional points is unstable with respect to $C^0$-norm of thevelocity for a $C^1$ small perturbation in the shape of the wall(even if the wall is still smooth). Then we seek a smooth transonicflow of Meyer type which satisfies physical boundary condition andwhose sonic points are exceptional in a de Laval nozzle. For such aflow, its sonic curve must be located at the throat of the nozzle andthe governing equation is strongly degenerate in the sense that thesonic curve is a characteristic degenerate boundary in thesubsonic-sonic region, while in the sonic-supersonic region allcharacteristics from sonic points coincide, which are the sonic curveand never approach the supersonic region. It is proved that thereexists uniquely such a smooth transonic flow near the throat of thenozzle, whose acceleration is Lipschitz continuous, if the wall ofthe nozzle is sufficiently flat. The works are jointed with ProfessorZhouping Xin.