Global existence and steady states of the density-suppressed motility model with strong Allee effect

发布时间：2024-09-10 作者：浏览次数：

Speaker:	王智诚	DateTime:	2024年9月12日（周四）下午14:30-16:30
Brief Introduction to Speaker: 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.、CVPDE、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）。		Place:	腾讯会议：583-717-670
Abstract:In this talk we consider a density-suppressed motility model with a strong Allee effect under the homogeneous Neumman boundary condition. We first establish the global existence of bounded classical solutions to a parabolic-parabolic system over a $N $-dimensional $\mathbf{(N\le 3)}$ bounded domain $\Omega$, as well as the global existence of bounded classical solutions to a parabolic-elliptic system over the multidimensional bounded domain $\Omega$ with smooth boundary. We then investigate the linear stability at the positive equilibria for the full parabolic case and parabolic-elliptic case respectively, and find the influence of Allee effect on the local stability of the equilibria. By treating the Allee effect as a bifurcation parameter, we focus on the one-dimensional stationary problem and obtain the existence of non-constant positive steady states, which corresponds to small perturbations from the constant equilibrium $(1,1)$. Furthermore, we present some properties through t...

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