2023西安电子科技大学非线性分析、微分方程与动力系统报告

报告题目：The stability of diverging traveling fronts and threshold phenomenon for the buffered bistable system

报告人：王智诚 教授兰州大学

照片：

邀请人：白振国

报告时间：2023年4月1日10：30-12：00

腾讯会议ID：343-657-492

报告人简介：王智诚，兰州大学best365亚洲版登录教授，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Trans. AMS、Arch. Rational Mech. Anal.、SIAM J. Math. Anal.、SIAM J. Appl. Math.、JMPA、Calc. Var. PDE、JDE、Nonlinearity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，主持或参加完成多项国家自然科学基金面上项目和重点项目，正在主持一项甘肃省基础研究创新群体项目和一项国家自然科学基金面上项目。目前担任InternationalJ. Bifurc. Chaos等杂志的编委（Associate editor）

报告摘要：In this talk we considera bistable system for calcium buffering. We first prove two kinds of stability of diverging traveling fronts of the degenerate system (All buffers do not diffuse): the local $C^0$-norm stability and the asymptotic stability. In particular, as for asymptotic stability, we prove a Liouville-type result by the sliding method, and then use the truncation technique to study the long-time behavior of diverging wave like solution. These stabilities imply that, under suitable conditions on the initial data, the solution locally uniformly approaches to the high equilibrium state $\left(1, \mathbf{b}_2\right)$. Then, by examining the behavior of solutions with one-parameter family of initial data, we show that the parameter-dependent solutions can be divided into three categories: convergence to the basal equilibrium state $\left(0,\mathbf{b}_0\right)$ for small parameter values, convergence to the high equilibrium state $\left(1,\mathbf{b}_2\right)$ for large parameter values, whereas neither of these behaviors occurs for intermediate parameter values. We refer to such phenomenon as threshold phenomenon. These intermediate parameter values are called threshold values, and the corresponding solutions are called threshold solutions. Finally, we present some important properties of the threshold solution and provide some numerical simulations.

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