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报告题目：Uniform Stability of Oscillatory Shocks for KdV-Burgers Equation
报 告 人：陈庚，堪萨斯大学 教授
报告摘要：We study viscous-dispersive shock waves with infinite oscillations of the Korteweg–de Vries–Burgers (KdVB) equation. First, we establish detail structures of the shock waves, including the rates at which the local extrema converge to the left end state towards the left far field. Then, by exploiting the structural properties of the shocks, we show the L2-contraction property of the shock profiles under arbitrarily large perturbations, up to time-dependent shifts. This property implies both time-asymptotic stability and uniform stability with respect to the viscosity and dispersion coefficients. This uniformity yields the existence of zero viscosity-dispersion limits, on which Riemann shocks are orbitally stable.
报告人简介：Geng Chen is the G. Bailey Price Professor and Director of Graduate Admissions in the Department of Mathematics at the University of Kansas. He received his PhD in Mathematics from the University of Massachusetts Amherst in 2010. Prior to his current role, he served as Associate and Assistant Professor at the University of Kansas and held postdoctoral positions at the Georgia Institute of Technology and Pennsylvania State University. His research spans analysis, partial differential equations, fluid dynamics, and mathematical physics, with a current focus on hyperbolic conservation laws, compressible Euler and Navier–Stokes equations, and nonlinear wave phenomena. His research has been continuously supported by the National Science Foundation since 2017.
报告时间：2026年4月13日 9：30-12：00
报告地点：文渊楼 B119
主办单位：数学与统计学院
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