星空讲堂：Stability of dispersive shock in KdV Burgers equation

报告人：沈燕南

报告题目：Stability of dispersive shock in KdV Burgers equation

报告时间：2026年6月18日（周四）14:00-16:00

报告地点：D2-220

摘要：We study the viscous-dispersive shock profile with infinite oscillations of the Korteweg–de Vries–Burgers (KdVB) equation. First, we establish detailed structures of the shock wave, including the rate at which the local extrema converge to the left end state towards the left far field. Then, by exploiting the structural properties of the shock, we show the L2 contraction property of the shock profile under arbitrarily large perturbations, up to a time-dependent shift. This result implies both time-asymptotic stability and uniform stability with respect to the viscosity and dispersion coefficients. This uniformity yields zero viscosity-dispersion limits.

报告人简介：沈燕南，美国University of Kansas数学系副教授，主要研究方向为动力系统、数学物理、数值分析和偏微分方程等。在Arch. Ration. Mech. Anal.、SIAM J. Math. Anal.、J. Differential Equations等国际著名学术期刊发表论文20余篇。