Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.01998 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916656390864896 |
|---|---|
| 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 |