报告题目:Traveling waves in a diffusive epidemic model with criss-cross mechanism

报告时间:2022年10月25日(星期二),16:30-17:30

报告地点:广东技术师范大学东校区工业中心605室

内容摘要:In this talk, we consider a reaction-diffusion system to describe the spread of infectious diseases within two population groups by self and criss-cross infection mechanism. Firstly, based on the eigenvalues, we give two methods for the calculation of the critical wave speed $c^*$. Secondly, by constructing a pair of upper-lower solutions and using the schauder's fixed-point theorem, we prove that the system admits positive traveling wave solutions, which connect the initialdisease-free equilibrium $(u_1^0, 0,u_3^0,0)$ at $t=-\infty$, but the traveling waves need not connect the final disease-free equilibrium $(u_1^*,0,u_3^*,0)$ at $t=+\infty$. Hence, we study the asymptotic behaviors of the traveling wave solutions to show that the traveling wave solutions converge to $(u_1^*,0,u_3^*,0)$ at $t=+\infty$. Finally, by the two-sided Laplace transform, we establish the non-existence of traveling waves for the model. The approach in this paper provides an effective method to deal with the existence of traveling wave solutions for the non-monotone reaction-diffusion systems consisting of four equations.

报告人简介:徐志庭，华南师范大学数学科学学院教授，博士研究生导师。研究方向为微分方程与动力系统。在J. Math. Pures. Appl.，Nonlinear Analysis: TMA.，Nonlinear Analysis: RWA.，IMA. J. Appl. Math.，J. Math. Anal. Anal.，Discrete Contin Dyn Sys. B等国际期刊上发表论文80余篇。已培养硕士研究生40余名，2007年获广东省自然科学进步奖（排名第三）。

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