Sharp estimates of the one-dimensional boundary control cost for parabolic systems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929229116997632 |
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| author | González-Burgos, Manuel Ouaili, Lydia |
| author_facet | González-Burgos, Manuel Ouaili, Lydia |
| contents | In this work we present new results on the cost of the boundary controllability of parabolic systems at time $T > 0$. In particular, we will study optimal estimates of the control cost at time $T$ ($T$ small enough) when the eigenvalues of the generator of the $C_0$ semigroup accumulate and do not satisfy a gap condition. The main ingredient we will use is the moment method combined with sharp estimates of the $L^2(0,T; \mathbb C)$-norm of the elements of biorthogonal families to complex exponentials. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_17349 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp estimates of the one-dimensional boundary control cost for parabolic systems González-Burgos, Manuel Ouaili, Lydia Optimization and Control Primary 93B05, 93B07 In this work we present new results on the cost of the boundary controllability of parabolic systems at time $T > 0$. In particular, we will study optimal estimates of the control cost at time $T$ ($T$ small enough) when the eigenvalues of the generator of the $C_0$ semigroup accumulate and do not satisfy a gap condition. The main ingredient we will use is the moment method combined with sharp estimates of the $L^2(0,T; \mathbb C)$-norm of the elements of biorthogonal families to complex exponentials. |
| title | Sharp estimates of the one-dimensional boundary control cost for parabolic systems |
| topic | Optimization and Control Primary 93B05, 93B07 |
| url | https://arxiv.org/abs/2401.17349 |