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arXiv · 2603.09263

$L^2$-contraction of Shock Waves for KdV-Burgers Equation

Geng Chen·Namhyun Eun·Moon-Jin Kang·Yannan Shen
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Abstract

The KdV-Burgers equation is a canonical model describing the interplay between nonlinearity, viscosity and dispersion, and it admits viscous-dispersive shocks as traveling wave solutions. In this paper, we establish an $L^2$-contraction property for viscous-dispersive shocks under arbitrarily large perturbations, up to a time-dependent shift. This yields time-asymptotic stability and uniform estimates with respect to the strengths of viscosity and dispersion. We present the proof for the monotone shocks, and introduce the companion work in [6] on the stability and structural properties of oscillatory shocks.

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Geng Chen, Namhyun Eun, Moon-Jin Kang, Yannan Shen. 2026-03-10. $L^2$-contraction of Shock Waves for KdV-Burgers Equation. https://arxiv.org/abs/2603.09263

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