题 目: Global Solvability and Large Time Behavior to a Chemotaxis Model with Nonlinear Diffusion
This talk is concerned with a chemotaxis model with with porous medium slow diffusion $\Delta u^m (m > 1)$. We consider this problem in a bounded domain of $R^3$ with zero-flux boundary condition, and it is shown that for any large initial datum, for any m > 1, the problem admits a global uniformly bounded weak solution。 Subsequently, the large time behavior of the solutions are also discussed. The methods and results of this paper are also applicable for the coupled chemotaxis-Stokes system. In particular, for the case without bacteria proliferation, the present results improved the work of Tao, Winkler et.al[2013,Ann. I. H. Poincare AN; 2015, CVPDE; 2018, JDE], and answered the open problem proposed by Winkler.
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。曾获教育部新世纪优秀人才支撑计划资助，主持了包括国家自然科学基金面上项目，广东省杰出青年基金在内的多项项目基金。