Stabilization of a perturbed quintic defocusing Schrödinger equation in $\mathbb{R}^{3}$
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909395520061440 |
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| author | Silva, Pablo Braz e Capistrano-Filho, Roberto de A. Carvalho, Jackellyny Dassy do Nascimento Ferreira, David dos Santos |
| author_facet | Silva, Pablo Braz e Capistrano-Filho, Roberto de A. Carvalho, Jackellyny Dassy do Nascimento Ferreira, David dos Santos |
| contents | This article addresses the stabilizability of a perturbed quintic defocusing Schrödinger equation in $\mathbb{R}^{3}$ at the $H^1$--energy level, considering the influence of a damping mechanism. More specifically, we establish a profile decomposition for both linear and nonlinear systems and use them to show that, under certain conditions, the sequence of nonlinear solutions can be effectively linearized. Lastly, through microlocal analysis techniques, we prove the local exponential stabilization of the solution to the perturbed Schrödinger equation in $\mathbb{R}^{3}$ showing an observability inequality for the solution of the system under consideration, which is the key result of this work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16976 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stabilization of a perturbed quintic defocusing Schrödinger equation in $\mathbb{R}^{3}$ Silva, Pablo Braz e Capistrano-Filho, Roberto de A. Carvalho, Jackellyny Dassy do Nascimento Ferreira, David dos Santos Analysis of PDEs Optimization and Control This article addresses the stabilizability of a perturbed quintic defocusing Schrödinger equation in $\mathbb{R}^{3}$ at the $H^1$--energy level, considering the influence of a damping mechanism. More specifically, we establish a profile decomposition for both linear and nonlinear systems and use them to show that, under certain conditions, the sequence of nonlinear solutions can be effectively linearized. Lastly, through microlocal analysis techniques, we prove the local exponential stabilization of the solution to the perturbed Schrödinger equation in $\mathbb{R}^{3}$ showing an observability inequality for the solution of the system under consideration, which is the key result of this work. |
| title | Stabilization of a perturbed quintic defocusing Schrödinger equation in $\mathbb{R}^{3}$ |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2410.16976 |