Stability for Oscillatory Shocks of KdV-Burgers Equation
ABSTRACT
It is well known that the Korteweg-de Vries-Burgers (KdVB) equation admits traveling wave solutions, referred to as viscous-dispersive shock waves.
When the dispersion dominates viscosity, the associated shock profiles exhibit infinitely many oscillations.
Although the KdVB equation serves a a canonical model incorporating nonlinearity, viscosity, and dispersion, the stability of these shock profiles-especially in the oscillatory regime-remains poorly understood.
In this talk, we discuss detailed structural properties of the shock profiles, and then prove an L^2 contraction property under arbitrarily large perturbations, up to a time-dependent shift.
Moreover, we also justify zero viscosity-dispersion limits.
This is a collaborative work with Geng Chen (University of Kansas), Moon-Jin Kang (KAIST), and Yannan Shen (University of Kansas).
