Conference Name: One Day Workshop on Applied PDEs
Organizations: Zhen Lei, Yi Zhou
Host: 数学科学学院
Venue: 光华东主楼1501
Opening Time: 2018年3月26日
Closing Time: 2018年3月26日

报告1:Some Properties of Solutions for the Heat Equation with sources

报 告 人:尹景学 教授



报告摘要:In this talk, we discuss the heat eqution with nonlinear sources. Some properties, such as the life span and periodic soltions, will be presented.



报告2:Lipschitz Continuous Subsonic-sonic Flows in General Nozzles

报告人:王春朋 教授



报告摘要:This talk concerns subsonic-sonic potential flows in two dimensional nozzles. For a finitely long symmetric nozzle which is suitably flat near the throat (where the cross section is smallest) and whose wall is parallel to the symmetric axis at its two endpoints, we formulate the subsonic-sonic flow problem by prescribing the flow angle at the inlet and the outlet. It is shown that there is a unique subsonic-sonic flow whose acceleration is bounded for such a problem. Moreover, its sonic points must occur at the wall or the throat. More precisely, there exists a critical value such that the flow is sonic on the whole throat if the height of the nozzle is not greater than this critical value, while the sonic points must be located at the wall if the height is greater than this value. There are similar results for infinitely long symmetric nozzles and the asymptotic behavior at the infinity of subsonic-sonic flows are shown. 


报告3:Global Classical Solution and Boundedness to a Chemotaxis-Haptotaxis Model with Re-modelling Mechanism

报告人:金春花 教授



报告摘要:We deal with a chemotaxis-haptotaxis model with re-establishment effect. We consider this problem in a bounded domain with zero-flux boundary conditions. Although the $L^\infty$-norm of the ECM density is easy to be obtained, the re-establishment mechanism still cause essential difficulty due to the deficiency of regularity for ECM. We use some iterative techniques to establish the $W^{1,\infty}$ bound of  uPA protease concentration, and further obtained the $L^\infty$ estimate of the cancer cell density. Using these a prior estimates, we finally established the existence of  global-in-time classical solution, which is bounded uniformly. The result of this paper fills the gap  of Tao,Winkler [JDE,2014] and Pang, Wang [JDE, 2017] in dimension 2 with logistic source, in the work of Tao,Winkler [JDE,2014] , the boundedness of the solution is left open; and in the work of Pang, Wang [JDE, 2017], the global existence and boundedness is established only for large proliferation rate. In particular,  the  global  solvability and boundedness of smooth solutions in dimension 3 has never been touched before, this work is the first attempt to solve this problem.


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Annual Speech Directory: No.3

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