Presentation Name: Global Classical Solution and Boundedness to a Chemotaxis-Haptotaxis Model with Re-modelling Mechanism
Presenter: 金春花 教授
Date: 2018-03-26
Location: 光华东主楼1501
Abstract:

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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