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 and Winkler, the boundedness of the solution is left open; and in the work of Pang and Wang, 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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