二维空间中含大扰动的振荡色散平面激波解的$L^2$压缩性
The $L^2$ contraction of solutions with large perturbation in multiple space dimensions from the oscillatory dispersive planar shock
AI总结：
该研究针对描述水波的KP方程与多维KdV-Burgers方程，在二维空间任意大扰动下，证明了其平面色散激波剖面的$L^2$压缩性，拓展了相关已有结论。
AI中文摘要：
本文针对描述水波的耗散型Kadomtsev-Petviashvili（KP）方程的平面振荡或单调色散激波剖面，以及多维Korteweg-de Vries（KdV）-Burgers方程，在二维空间中任意大扰动下、直至依赖Lipschitz时间的平移，证明了其$L^2$压缩性。该稳定性结果拓展了Chen、Eun、Kang和Shen近期两篇关于KdV-Burgers方程$L^2$压缩性的论文的结论。
英文摘要：
In this paper, we show the $L^2$ contraction property of the planar oscillatory or monotone dispersive shock profiles of the dissipative Kadomtsev-Petviashvili (KP) equation modelling water waves and the multi-dimensional Korteweg-de Vries (KdV) Burgers equation under arbitrarily large perturbations in two space dimensions, up to Lipschitz time-dependent shifts. This stability result extends the results of two recent papers by Chen, Eun, Kang, and Shen on $L^2$ contraction for the KdV-Burgers equation.
