Small-time approximate controllability for the nonlinear complex Ginzburg-Landau equation with bilinear control
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908734430642176 |
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| author | Zeng, Xingwu Zhang, Can |
| author_facet | Zeng, Xingwu Zhang, Can |
| contents | In this paper, we consider the bilinear approximate controllability for the complex Ginzburg-Landau (CGL) equation with a power-type nonlinearity of any integer degree on a torus of arbitrary space dimension. Under a saturation hypothesis on the control operator, we show the small-time global controllability of the CGL equation. The proof is obtained by developing a multiplicative version of a geometric control approach, introduced by Agrachev and Sarychev in \cite{AS05,AS06}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22512 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Small-time approximate controllability for the nonlinear complex Ginzburg-Landau equation with bilinear control Zeng, Xingwu Zhang, Can Optimization and Control Analysis of PDEs In this paper, we consider the bilinear approximate controllability for the complex Ginzburg-Landau (CGL) equation with a power-type nonlinearity of any integer degree on a torus of arbitrary space dimension. Under a saturation hypothesis on the control operator, we show the small-time global controllability of the CGL equation. The proof is obtained by developing a multiplicative version of a geometric control approach, introduced by Agrachev and Sarychev in \cite{AS05,AS06}. |
| title | Small-time approximate controllability for the nonlinear complex Ginzburg-Landau equation with bilinear control |
| topic | Optimization and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2512.22512 |