报告题目：Global Classical Solution and Boundedness to a Chemotaxis-Haptotaxis Model with Re-modeling Mechanisms
报告人：金春花教授（华南师范大学）
报告时间：2018年1月4日（星期四） 13：00-14：00
报告地点：2B-303
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.
报告人简介：金春花，华南师范大学数学科学学院教授、博士生导师；目前的研究兴趣主要为生物数学中的偏微分方程；先后主持国家自然科学基金面上项目、国家自然科学基金青年基金项目、广东省自然科学杰出青年基金、 教育部博士点专项基金、 中国博士后科学基金特别资助、中国博士后科学基金一等资助等；获中国数学会钟家庆数学奖 、教育部自然科学奖二等奖(第四完成人)、吉林省优秀博士论文、全国优秀博士学位论文提名奖、香江学者奖；入选广东特支计划百千万青年工程拔尖人才项目、 广东省高等学校优秀青年教师培养计划、 教育部新世纪优秀人才支持计划等；已在JDE、Nonlinearity|、DCDS、ZAMP等重要数学期刊上发表学术论文50余篇。