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Main Authors: Gallego, F. A., Martinez, V. H. Gonzalez, Grajales, J. C. Muñoz
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2410.01998
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author Gallego, F. A.
Martinez, V. H. Gonzalez
Grajales, J. C. Muñoz
author_facet Gallego, F. A.
Martinez, V. H. Gonzalez
Grajales, J. C. Muñoz
contents In this paper, we present results on the energy decay of the BBM-KP equations (I and II) posed on $\R^2$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2410_01998
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Global Stabilization for the BBM-KP equations on R2
Gallego, F. A.
Martinez, V. H. Gonzalez
Grajales, J. C. Muñoz
Analysis of PDEs
Optimization and Control
In this paper, we present results on the energy decay of the BBM-KP equations (I and II) posed on $\R^2$ 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.
title Global Stabilization for the BBM-KP equations on R2
topic Analysis of PDEs
Optimization and Control
url https://arxiv.org/abs/2410.01998