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人力资源部教师发展中心“学者论坛”第87期安排如下,欢迎广大师生参加:
一、主 题:Global Classical Solution and Boundedness to a Chemotaxis-Haptotaxis Model with Re-modelling Mechanisms
二、主讲人:中国数学会钟家庆数学奖获得者 金春花 教授
三、时 间:2018年1月4日(周四)上午10:00
四、地 点:清水河校区主楼A1-407
五、主持人:数学科学学院 向昭银 教授
六、交流内容:
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.
七、主讲人简介:
金春花,华南师范大学数学科学学院教授、博士生导师,目前的研究兴趣为主要为生物数学中的偏微分方程。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、广州市珠江科技新星项目等。已在JDE、Nonlinearity|、DCDS、ZAMP等重要数学期刊上发表学术论文50余篇。
八、主办单位:人力资源部教师发展中心
承办单位:数学科学学院
人力资源部教师发展中心
2017年12月29日
编辑:胡武辉 / 审核:林坤 / 发布:林坤