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华南师范大学数学科学学院金春花教授学术报告

发布:2018-01-04 10:00       作者:admin      来源:未知

报告题目:Global Classical Solution and Boundedness to a Chemotaxis-Haptotaxis Model with Re-modelling Mechanisms

 

报告人:金春花 教授(华南师范大学)

 

报告时间:2018.01.04(周四)上午1000-1100

 

报告地点:清水河校区主楼A1 - 407

 

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 TaoWinkler [JDE2014] and Pang, Wang [JDE, 2017] in dimension 2 with logistic source, in the work of TaoWinkler [JDE2014] , 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JDENonlinearity|DCDSZAMP等重要数学期刊上发表学术论文50余篇


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