讲座主题：Prevention of infinite-time blowup in a Keller-Segel system with density-suppressed motility

专家姓名：江杰

工作单位：中国科学院精密测量科学与技术创新研究院

讲座时间：2025年05月31日 14:30-15:50

讲座地点：烟台大学承先图书馆报告厅

主办单位：烟台大学数学与信息科学学院

内容摘要：

In this talk, we consider an initial-Neumann boundary value problem for a Keller-Segel system with non-local Fokker-Planck type diffusion and source terms. Infinite-time blowup of the classical solution was previously observed for its source-free version when dimension N≥2. In this talk, we will report our recent result that with any source term involving a slightly super-linear degradation effect on the density, of a growth order of at most, the classical solution is uniformly-in-time bounded when N≤3, thus preventing the infinite-time explosion detected in the source-free counter-part. By contrast, we recall that there are finite-time blowups in Keller-Segel system with Fick type diffusion even when slightly super-linear degradation gets involved. Thus, our result reveals an important difference between Fokker-Planck type diffusion and Fick type diffusion in Keller-Segel models. We will first outline the comparison method developed by the speaker to study the homogeneous problem and we review some previous results concerning global boundedness as well as infinite blowups. Then, we show that an improved comparison argument by introducing a new auxiliary variable, together with a construction of an entropy-like inequality will yield to the desired blowup-prevention result.

主讲人介绍：

江杰，2004年毕业于山东大学数学与系统科学学院基地班，2009年于复旦大学数学科学学院获得理学博士学位，师从郑宋穆教授. 2009年到2011年在北京应用物理与计算数学研究所郭柏灵院士指导下从事博士后工作. 主要研究趋化方程、相场-流体方程组等非线性发展方程整体解的适定性、有界性、渐近性、爆破解等相关问题. 目前在CPDE, CVPDE, JDE, SIMA, Nonlinearity等国际数学刊物正式发表SCI论文31篇(通讯作者27篇). 获得2021年度中国科学院精密测量院突出科技成果奖，2023年湖北省工业与应用数学学会优秀青年学者奖. 主持多项国家自然科学基金等课题。