On the strongly competitive case in a fully parabolic

报告题目：On the strongly competitive case in a fully parabolic two-species chemotaxis system with Lotka-Volterra competitive kinetics

报 告 人：穆春来  教授

报告时间：5月12日14:30-16:30

报告地点：明理楼C302B

报告人简介：

穆春来，教授，重庆大学数学与统计学院院长。穆教授主要从事非线性偏微分方程和生物数学研究；先后入选“教育部新世纪优秀人才”计划、重庆市学术与技术带头人、重庆市英才计划领军人才；承担了国家自然科学基金、教育部新世纪优秀人才基金、重庆市自然科学重点基金等；2019年获教育部自然科学奖二等奖，2015年获得重庆市自然科学奖二等奖，2014年获得国家教学成果二等奖；已在M3AS, JDE, J. Nonlinear Sci，JDDE，Proc. Roy. Soc. Edingh-A, DCDS，中国科学，数学学报等国内外重要数学期刊发表论文多篇。

报告内容摘要：

This work considers a two-species chemotaxis system with Lotka-Volterra competitive kinetic functional response term in a bounded domain with smooth boundary. We proved global bounded solutions to the system in high dimensions without the convexity of the domain. Moreover, by constructing appropriate Lyapunov functionals, it is proved that the solution convergences to the semitrivial steady state under strong competition if the growth coefficients of two species are appropriately large. Furthermore, the linear stability analysis is performed to find the possible patterning regimes, outside the stability parameters regime, for both semi-trivial and coexistence steady states, our numerical simulations show that non-constant steady states and spatially inhomogeneous temporal periodic patterns are all possible.

主办单位：理学院、人工智能研究院、非线性动力系统研究所、数理力学研究中心 、科学技术发展研究院