Long-Time Dynamics of the Zakharov-Kuznetsov Equation
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908694708486144 |
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| author | Filho, Roberto de A. Capistrano Nascimento, Ailton |
| author_facet | Filho, Roberto de A. Capistrano Nascimento, Ailton |
| contents | This manuscript presents the results of stabilization for the Zakharov--Kuznetsov equation, a two-dimensional Korteweg--de Vries-type equation. We provide rigorous proofs using two different approaches, showing that when a damping mechanism and an internal delay term (anti-damping) are introduced, the solutions of the Zakharov--Kuznetsov equation exhibit both local and global exponential stabilization properties. A significant contribution of our work is the determination of the optimal constant and the minimal time required to ensure exponential decay of the energy associated with this two-dimensional system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17830 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Long-Time Dynamics of the Zakharov-Kuznetsov Equation Filho, Roberto de A. Capistrano Nascimento, Ailton Analysis of PDEs This manuscript presents the results of stabilization for the Zakharov--Kuznetsov equation, a two-dimensional Korteweg--de Vries-type equation. We provide rigorous proofs using two different approaches, showing that when a damping mechanism and an internal delay term (anti-damping) are introduced, the solutions of the Zakharov--Kuznetsov equation exhibit both local and global exponential stabilization properties. A significant contribution of our work is the determination of the optimal constant and the minimal time required to ensure exponential decay of the energy associated with this two-dimensional system. |
| title | Long-Time Dynamics of the Zakharov-Kuznetsov Equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.17830 |