analysis of partial differential equations

The $L^{2}$ contraction of solutions with large perturbation in multiple space dimensions from the oscillatory dispersive planar shock

arXiv:2607.27118

summary

The paper proves that planar oscillatory or monotone dispersive shock profiles of the dissipative Kadomtsev‑Petviashvili equation and the multi‑dimensional KdV‑Burgers equation contract in the L² norm even under arbitrarily large perturbations, allowing for time‑dependent Lipschitz shifts.

Abstract

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.

Topics & keywords

#shock waves #dispersive equations #stability analysis #L2 contraction #multi-dimensional PDEsL² contractionKadomtsev-Petviashvili equationKdV-Burgers equationplanar shocklarge perturbationsLipschitz shift

The L2 contraction of solutions with large perturbation in multiple space dimensions from the oscillatory dispersive planar shock

Abstract

Topics & keywords

The $L^{2}$ contraction of solutions with large perturbation in multiple space dimensions from the oscillatory dispersive planar shock