报告题目：Patterns of the density-suppressed motility model

报告人：马满军教授

报告地点：腾讯会议 852 514 129

报告时间：2021年7月5日19：30-21：30

摘要: In this work, we first explore the stationary problem of a density-suppressed motility (DSM) model where the diffusion rate of the bacterial cells is a decreasing function (motility function) of the concentration of a chemical secreted by bacteria themselves.We show that the DSM model does not admit non-constant steady states if either the chemical diffusion rate or the intrinsic growth rate of bacteria is large. We also prove that when the decay of the motility function is sub-linear or linear, the DSM model does not admit non-constant steady states if either the chemical diffusion rate or the intrinsic growth rate of bacteria is small. Outside these non-existence parameter regimes, we show that the DSM model will have non-constant steady states under some constraints on the parameters. Furthermore we numerically find the stable stationary patterns only when the parameter values are close to the critical regime. Finally by performing a delicate multiple-scale analysis, we derive that the DSM model may generate propagating oscillatory waves whose amplitude is governed by an explicit Ginzburg-Landau equation, which is further verified by numerical simulations.

报告人介绍：马满军，浙江理工大学教授, 博士生导师,美国《数学评论》评论员；1989年于湖南师范大学获得数学专业学士学位；分别于1999年与2005年在湖南大学获得应用数学专业硕士、博士学位。美国圣地亚哥州立大学非线性动力系统中心访问学者；自2008年以来，多次应邀访问加拿大纪念大学、香港理工大学，进行合作研究。主要从事微分方程存在性与稳定性理论及动力系统非线性波理论的研究，并且利用相关理论研究Bose-Einstein凝聚体中孤立子、生物生态学、化学等背景学科领域数学模型的动力学性质。在国际权威期刊《J. Differential Equations》、《SIAM Journal on Applied Mathematics》、《SIAM J. Math. Anal.》《Nonlinearity》、《Discrete and Continuous Dynamical Systems - Series B》、《Analysis and Applications》、《Phys. D》等发表学术论文50余篇。主持国家自然科学基金面上项目、国际合作与交流项目多项。