【理学院】Asymptotic stability of non-monotone traveling waves for time-delayed non-local dispersion equations

报告题目：Asymptotic stability of non-monotone traveling waves for time-delayed non-local dispersion equations

报告摘要：This talk is concerned with the stability of non-monotone traveling waves to a nonlocal dispersion equation with time-delay, a time-delayed integro-differential equation. When the equation is crossing-monostable, the equation and the traveling waves both loss their monotonicity, and the traveling waves are oscillating as the time-delay is big. In this paper, we prove that all non-critical traveling waves (the wave speed is greater than the minimum speed), including those oscillatory waves, are time-exponentially stable, when the initial perturbations around the waves are small. The adopted approach is still the technical weighted-energy method but with a new development. Numerical simulations in different cases are also carried out, which further confirm our theoretical result. Finally, as a corollary of our stability result, we immediately obtain the uniqueness of the traveling waves for the non-monotone integro-differential equation, which was open so far as we know.

报告人：梅茗，教授（Champlain College St-Lambert & McGill University, Canada）

时 间：6月28日（周二）下午15：15—16：15

地 点：18-918（理学院会议室）

人物名片：梅茗教授是Champlain College St-Lambert 的全职教授，McGill大学兼职教授，吉林省“长白山学者”讲座教授，“东师学者”讲座教授。目前担任四个SCI期刊的副主编和编委，50余个国际杂志的审稿人，发表高水平学术论文70余篇，主要研究论文发表在 Arch. Rational Mech. Anal.， Commun. Partial Differential Equations，SIAM Journal of Applied Mathematics，Journal of Differential Equations等杂志上。多次应邀参加国际数学大会并作大会报告，并主持多项加拿大国家基金。详见梅教授网页：http://www.math.mcgill.ca/~mei/