报告题目：Boundedness of global classical solutions for a chemotaxis system with signal-dependent motility and nutrient consumption

主讲人：李玉祥教授

单位：东南大学

时间：12月11日14:30

地点：学院二楼会议室

摘要：In this talk we consider the initial-boundary value problem for a Keller-Segel system with the logistic term au-bu^σ. The Keller-Segel system describes directional movement of bacteria caused by the signal-dependent diffusion and the starvation driven diffusion. We prove that

1）The signal production equation is elliptic. Ifσ>2 orσ=2 and b is sufficiently large, then the classical solutions of the system are globally bounded in dimensions N≥3. On the other hand, ifσ∈(1,2], we obtain the global existence of weak solutions to the system when N≥3.

2）The signal production equation is parabolic. Ifσ>2 orσ=2 and b is sufficiently large, then the classical solutions of the system are globally bounded when N=3. On the other hand, ifσ∈(1,2), we obtain the global existence of weak solutions to the system when N≥3. In comparison with the case that the signal production equation is elliptic, hereσ≠2.

3）When the signal production equation is elliptic or parabolic, ifσ>1, we obtain the uniform boundedness of global classical solutions to the system with N=2.

简介：李玉祥，东南大学数学学院教授，博士生导师，江苏省优秀博士学位论文指导教师，教育部自然科学二等奖获得者。研究方向包括非线性抛物型方程、KPZ方程、趋化方程，在解的有限时刻爆破、整体存在性和渐近性等方面，获得了一系列结果。在Math. Ann.、CMP、Nonlinearity、M3AS、JDE、Ann. Henri Poincaré、European J. Appl. Math.等刊物发表论文60余篇，主持承担4项国家自然科学基金项目。