报告题目：Traveling wave solutions to the competitive model with density-suppressed motility

报告人：王智诚教授 兰州大学

报告时间：2024年5月12日（星期日），14：30—15：30

报告地点：兴庆校区数学楼2-3会议室

报告摘要：In this talk, we investigate the invasion and exclusion phenomenon of a foreign bacterium species with density-suppressed motility on a local bacterium species that only has random diffusion. Through introducing auxiliary problem, constructing relaxed super- and sub-solutions with spatially inhomogeneous decay rates and using energy estimation method, under appropriate parameter conditions, the existence of traveling wave solutions connecting two constant equilibrium points $(0,1,0)$ and $(1,0,1)$ with wave speed $c> 2\sqrt{1-a}$ is established, while such traveling wave solutions do not exist when $c<2\sqrt{1-a}$. Moreover, the existence of traveling wave solution with speed $c=2\sqrt{1-a}$ connecting $(0,1,0)$ and $(1,0,1)$ is obtained by a limiting process and energy estimations. Finally, we discuss the possible selection of wave profiles/speeds using linearization method and the possible impact of density-suppressed motility term on asymptotic spreading speed of traveling wave by numerical simulation.

个人简介：王智诚，兰州大学数学与统计学院教授，兰州大学“萃英学者”特聘教授，博士生导师。1994年本科毕业于西北师范大学，2007年在兰州大学获理学博士学位。主要成果发表在Arch. Rational Mech. Anal.、JMPA、Trans. AMS、SIAM J. Math. Anal.、SIAM J. Appl. Math.、Calc. Var. PDE、J. d’Anal. Math.、JDE、JDDE、Nonlinearity、J. Nonlinear Sci. 等杂志上。2010年入选教育部新世纪优秀人才支持计划，2011和2019年分别获得甘肃省自然科学二等奖，2016年入选甘肃省飞天学者特聘教授，主持完成多项国家自然科学基金面上项目。目前担任两个SCI杂志International J. Bifurc. Chaos 和Mathematical Biosciences and Engineering (MBE) 的编委（Associate editor）。