Duality for Evolutionary Equations with Applications to Null Controllability
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914246142459904 |
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| author | Buchinger, Andreas Seifert, Christian |
| author_facet | Buchinger, Andreas Seifert, Christian |
| contents | We study evolutionary equations in exponentially weighted $\mathrm{L}^{2}$-spaces as introduced by Picard in 2009. First, for a given evolutionary equation, we explicitly describe the $ν$-adjoint system, which turns out to describe a system backwards in time. We prove well-posedness for the $ν$-adjoint system. We then apply the thus obtained duality to introduce and study notions of null-controllability for evolutionary equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14239 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Duality for Evolutionary Equations with Applications to Null Controllability Buchinger, Andreas Seifert, Christian Analysis of PDEs Functional Analysis Optimization and Control 35Axx, 35F35, 35M10, 47F05, 47N20 We study evolutionary equations in exponentially weighted $\mathrm{L}^{2}$-spaces as introduced by Picard in 2009. First, for a given evolutionary equation, we explicitly describe the $ν$-adjoint system, which turns out to describe a system backwards in time. We prove well-posedness for the $ν$-adjoint system. We then apply the thus obtained duality to introduce and study notions of null-controllability for evolutionary equations. |
| title | Duality for Evolutionary Equations with Applications to Null Controllability |
| topic | Analysis of PDEs Functional Analysis Optimization and Control 35Axx, 35F35, 35M10, 47F05, 47N20 |
| url | https://arxiv.org/abs/2411.14239 |