Asymptotic behavior of null-controllablity cost for parabolic equations with vanishing diffusivity and a transport term
In this paper we study the null controllability cost of a transport-diffusion system under Robin boundary conditions with distributed control and in which the transport coefficient is a gradient field. First, we provide some conditions on transport coefficient and boundary potential to show that the...
| Autores: | ; ; ; |
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| Tipo de documento: | Artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universidad del País Vasco |
| Repositorio: | Addi. Archivo Digital para la Docencia y la Investigación |
| OAI Identifier: | oai:addi.ehu.eus:10810/73738 |
| Acceso en línea: | http://hdl.handle.net/10810/73738 |
| Nivel de acceso: | Acceso abierto |
| Palabra clave: | Carleman estimates Uniform controllability Transport equation Singular limits Cost control Spectral decomposition |
| _version_ | 1878729441198211072 |
|---|---|
| author | Et-Tahri, Fouad |
| author2 | Barcena Petisco, Jon Asier Boutaayamou, Idriss Maniar, Lahcen |
| author2_role | author author author |
| author_browse | Barcena Petisco, Jon Asier Boutaayamou, Idriss Et-Tahri, Fouad Maniar, Lahcen |
| author_facet | Et-Tahri, Fouad Barcena Petisco, Jon Asier Boutaayamou, Idriss Maniar, Lahcen |
| author_role | author |
| collection | Addi. Archivo Digital para la Docencia y la Investigación |
| description | In this paper we study the null controllability cost of a transport-diffusion system under Robin boundary conditions with distributed control and in which the transport coefficient is a gradient field. First, we provide some conditions on transport coefficient and boundary potential to show that the control cost decays exponentially when the viscosity vanishes and the control time is sufficiently large. On the other hand, if the range of the control region by the transport flow does not cover that of $\Omega$, we prove that the control cost explodes exponentially for the Neumann boundary conditions case with vanishing viscosity and all control time. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_07ffea0a3a4e20df04c06b63c3560c8a |
| institution | Universidad del País Vasco |
| instname_str | Universidad del País Vasco |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:addi.ehu.eus:10810/73738 |
| publishDate | 2024 |
| publishDateSort | 2024 |
| publisher | EDP Sciences |
| publisherStr | EDP Sciences |
| reponame_str | Addi. Archivo Digital para la Docencia y la Investigación |
| spelling | Asymptotic behavior of null-controllablity cost for parabolic equations with vanishing diffusivity and a transport term Et-Tahri, Fouad Barcena Petisco, Jon Asier Boutaayamou, Idriss Maniar, Lahcen Carleman estimates Uniform controllability Transport equation Singular limits Cost control Spectral decomposition In this paper we study the null controllability cost of a transport-diffusion system under Robin boundary conditions with distributed control and in which the transport coefficient is a gradient field. First, we provide some conditions on transport coefficient and boundary potential to show that the control cost decays exponentially when the viscosity vanishes and the control time is sufficiently large. On the other hand, if the range of the control region by the transport flow does not cover that of $\Omega$, we prove that the control cost explodes exponentially for the Neumann boundary conditions case with vanishing viscosity and all control time. J.A.B.P. was supported by the Grant PID2021-126813NB-I00 funded by MICIU/AEI/10.13039/501100011033 and by “ERDF A way of making Europe” and by the grant IT1615-22 funded by the Basque Government. EDP Sciences http://hdl.handle.net/10810/73738 |
| spellingShingle | Asymptotic behavior of null-controllablity cost for parabolic equations with vanishing diffusivity and a transport term Et-Tahri, Fouad Carleman estimates Uniform controllability Transport equation Singular limits Cost control Spectral decomposition |
| title | Asymptotic behavior of null-controllablity cost for parabolic equations with vanishing diffusivity and a transport term |
| title_full | Asymptotic behavior of null-controllablity cost for parabolic equations with vanishing diffusivity and a transport term |
| title_fullStr | Asymptotic behavior of null-controllablity cost for parabolic equations with vanishing diffusivity and a transport term |
| title_full_unstemmed | Asymptotic behavior of null-controllablity cost for parabolic equations with vanishing diffusivity and a transport term |
| title_short | Asymptotic behavior of null-controllablity cost for parabolic equations with vanishing diffusivity and a transport term |
| title_sort | Asymptotic behavior of null-controllablity cost for parabolic equations with vanishing diffusivity and a transport term |
| topic | Carleman estimates Uniform controllability Transport equation Singular limits Cost control Spectral decomposition |
| topic_facet | Carleman estimates Uniform controllability Transport equation Singular limits Cost control Spectral decomposition |
| url | http://hdl.handle.net/10810/73738 |