R2上的BBM-KP方程的全局稳定化
偏微分方程分析
2025-03-20 v2 最优化与控制
摘要
In this paper, we present results on the energy decay of the BBM-KP equations (I and II) posed on with localized damping. This model offers an alternative to the KP equations, analogous to how the regularized long-wave equation relates to the classical Korteweg-de Vries (KdV) equation. We show that the energy associated with the Cauchy problem decays exponentially when a localized dissipative mechanism is present in a subdomain. Finally, we validate the theoretical results on the exponential stabilization of solutions to the BBM-KP equations with damping through numerical experiments using a spectral-finite difference scheme.
引用
@article{arxiv.2410.01998,
title = {Global Stabilization for the BBM-KP equations on R2},
author = {F. A. Gallego and V. H. Gonzalez Martinez and J. C. Muñoz Grajales},
journal= {arXiv preprint arXiv:2410.01998},
year = {2025}
}