$L^2$-contraction of Shock Waves for KdV-Burgers Equation
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910047395643392 |
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| author | Chen, Geng Eun, Namhyun Kang, Moon-Jin Shen, Yannan |
| author_facet | Chen, Geng Eun, Namhyun Kang, Moon-Jin Shen, Yannan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09263 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $L^2$-contraction of Shock Waves for KdV-Burgers Equation Chen, Geng Eun, Namhyun Kang, Moon-Jin Shen, Yannan Analysis of PDEs 35B35, 35Q53, 35L67, 76L05 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. |
| title | $L^2$-contraction of Shock Waves for KdV-Burgers Equation |
| topic | Analysis of PDEs 35B35, 35Q53, 35L67, 76L05 |
| url | https://arxiv.org/abs/2603.09263 |