Introduction to time-delayed reaction-diffusion equations

時滯反應擴散方程引介

報告人：梅 茗 教授

主持人：張曉穎院長、胡海豐、祝英杰

時 間：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 點：線上，騰訊會議號308934640

主辦單位：長春大學理學院

報告人簡介：梅茗，加拿大McGill大學及Champlain學院教授, 博士生導師。意大利L’Aquila大學客座教授，日本金澤大學合作教授，吉林省“長白山學者”講座教授，以及東北師范大學“東師學者”講座教授。主要從事流體力學中偏微分方程和生物數學中帶時滯反應擴散方程研究，在ARMA, SIAM, JDE, Commun.PDEs 等高水平雜志上發表論文100多篇，其中有關帶時滯反應擴散方程行波解穩定性的多篇系列性研究論文一直是ESI的高被引論文。梅茗教授是多家SCI國際數學雜志的編委，也是SlAM J Math Anal 和J Diff Equa等重要刊物的top author, 并一直承擔加拿大自然科學基金項目，魁北克省自然科學基金項目，及魁北克省大專院校國際局的基金項目。

觀點綜述：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.