Introduction to time-delayed reaction-diffusion equations

时滞反应扩散方程引介

报告人：梅 茗 教授

主持人：张晓颖院长、胡海丰、祝英杰

时 间：2024年1月29日星期一，上午09:00 – 11:00，

Lecture 1: Introduction to time-delayed reaction-diffusion equations

Lecture 2: Linear reaction-diffusion equations with delay

2024年1月29日星期一，下午14:00 – 16:00,

Lecture 3: Nonlinear reaction-diffusion equations with delay: Threshold convergence (part 1)

Lecture 4: Nonlinear reaction-diffusion equations with delay: Threshold convergence (part 2)

2024年1月30日星期二，上午09:00 – 11:00，

Lecture 5: Existence of Traveling waves

Lecture 6: Stability of Traveling waves: monotonic wavefronts

2024年1月30日星期二，下午14:00 – 16:00,

Lecture 7: Stability of Traveling waves: oscillating wavefronts

Lecture 8: Degenerate diffusion equations with time-delay

地 点：线上，腾讯会议号308934640

主办单位：长春大学理学院

报告人简介：梅茗，加拿大McGill大学及Champlain学院教授, 博士生导师。意大利L’Aquila大学客座教授，日本金泽大学合作教授，吉林省“长白山学者”讲座教授，以及东北师范大学“东师学者”讲座教授。主要从事流体力学中偏微分方程和生物数学中带时滞反应扩散方程研究，在ARMA, SIAM, JDE, Commun.PDEs 等高水平杂志上发表论文100多篇，其中有关带时滞反应扩散方程行波解稳定性的多篇系列性研究论文一直是ESI的高被引论文。梅茗教授是多家SCI国际数学杂志的编委，也是SlAM J Math Anal 和J Diff Equa等重要刊物的top author, 并一直承担加拿大自然科学基金项目，魁北克省自然科学基金项目，及魁北克省大专院校国际局的基金项目。

观点综述：In thisseries of academic lectures, we briefly introduce time-delayed reaction-diffusion equations in population dynamics and the latest progress. First of all, we introduce the modeling equations arising from species populations with age-structure in ecology, such as Nicholson’s blowflies equation, Mackey-Glass equation, nonlocal diffusion equation, nonlocal dispersion equation, Fisher-KPP equation with delay, Huxley equation with delay, and so on. The significant difference between the regular reaction-diffusion equations and the time-delayed reaction-diffusion equations will be also emphasized. Then we introduce the theory related to the existence and uniqueness of traveling waves to the time-delayed reaction-diffusion equations, particularly, when the time-delay is large, different from the regular reaction-diffusion equations without delay, the time-delay will cause the waves to be oscillating. In particular, we focus on the stability of traveling waves, particularly, the oscillating traveling waves. We will introduce different analysis methods for treating stability of wavefronts, including the monotone method, squeeze technique, Fourier transform, weighted energy method, spectral analysis method, and so on. A lot of numerical simulations in different cases will be introduced, too. These academic lectures are designed for graduates and young researchers with a background in partial different equations. The main aim is to introduce the basic theory in the topic of reaction-diffusion equations with delay as well as the frontier research progress, and to enhance the research interest for the graduates and young researchers and to encourage them to involve in.