Observability for heat equations with time-dependent analytic memory
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866909398442442752 |
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| author | Wang, Gengsheng Zhang, Yubiao Zuazua, Enrique |
| author_facet | Wang, Gengsheng Zhang, Yubiao Zuazua, Enrique |
| contents | This paper presents a complete analysis of the observability property of heat equations with time-dependent real analytic memory kernels. More precisely, we characterize the geometry of the space-time measurable observation sets ensuring sharp observability inequalities, which are relevant both for control and inverse problems purposes.
Despite the abundant literature on the observation of heat-like equations, existing methods do not apply to models involving memory terms.
We present a new methodology and observation strategy, relying on the decomposition of the flow, the time-analyticity of solutions and the propagation of singularities. This allows us to obtain a sufficient and necessary geometric condition on the measurable observation sets for sharp two-sided observability inequalities. In addition, some applications to control and relevant open problems are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_10615 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Observability for heat equations with time-dependent analytic memory Wang, Gengsheng Zhang, Yubiao Zuazua, Enrique Optimization and Control 93B07 93B05 45K05 This paper presents a complete analysis of the observability property of heat equations with time-dependent real analytic memory kernels. More precisely, we characterize the geometry of the space-time measurable observation sets ensuring sharp observability inequalities, which are relevant both for control and inverse problems purposes. Despite the abundant literature on the observation of heat-like equations, existing methods do not apply to models involving memory terms. We present a new methodology and observation strategy, relying on the decomposition of the flow, the time-analyticity of solutions and the propagation of singularities. This allows us to obtain a sufficient and necessary geometric condition on the measurable observation sets for sharp two-sided observability inequalities. In addition, some applications to control and relevant open problems are presented. |
| title | Observability for heat equations with time-dependent analytic memory |
| topic | Optimization and Control 93B07 93B05 45K05 |
| url | https://arxiv.org/abs/2101.10615 |