Control and homogenization of a system of coupled parabolic equations with an oscillating coefficient
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910398403313664 |
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| author | Jena, Vaibhav Kumar Sufian, Abu |
| author_facet | Jena, Vaibhav Kumar Sufian, Abu |
| contents | In this article, we study the uniform null controllability problem for a system of coupled parabolic equations with an oscillating coefficient. This is done in three steps -- first, we study the spectral properties of an elliptic operator; second, we allow the system to evolve freely and obtain the required decay; third, we use a Carleman estimate to prove a suitable observability result. This uniform null controllability property is then used to homogenize the associated coupled parabolic system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03335 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Control and homogenization of a system of coupled parabolic equations with an oscillating coefficient Jena, Vaibhav Kumar Sufian, Abu Analysis of PDEs 93B05, 93B07, 93B60, 35K05, 35P15 In this article, we study the uniform null controllability problem for a system of coupled parabolic equations with an oscillating coefficient. This is done in three steps -- first, we study the spectral properties of an elliptic operator; second, we allow the system to evolve freely and obtain the required decay; third, we use a Carleman estimate to prove a suitable observability result. This uniform null controllability property is then used to homogenize the associated coupled parabolic system. |
| title | Control and homogenization of a system of coupled parabolic equations with an oscillating coefficient |
| topic | Analysis of PDEs 93B05, 93B07, 93B60, 35K05, 35P15 |
| url | https://arxiv.org/abs/2404.03335 |