Observability Estimate for the Fractional Order Parabolic Equations on Measurable Sets
We establish an observability estimate for the fractional order parabolic equations evolved in a bounded domain Ω of ℝn. The observation region is F×ω, where ω and F are measurable subsets of Ω and (0,T), respectively, with positive measure. This inequality is equivalent to the null controllable pro...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/361904 |
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| _version_ | 1832566614900342784 |
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| author | Guojie Zheng M. Montaz Ali |
| author_facet | Guojie Zheng M. Montaz Ali |
| author_sort | Guojie Zheng |
| collection | DOAJ |
| description | We establish an observability estimate for the fractional order parabolic equations evolved in a bounded domain Ω of ℝn. The observation region is F×ω, where ω and F are measurable subsets of Ω and (0,T), respectively, with positive measure. This inequality is equivalent to the null controllable property for a linear controlled fractional order parabolic equation. The building of this estimate is based on the Lebeau-Robbiano strategy and a delicate result in measure theory provided in Phung and Wang (2013). |
| format | Article |
| id | doaj-art-5aba7e5908c14811a77b3315cba1b7e7 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5aba7e5908c14811a77b3315cba1b7e72025-02-03T01:03:37ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/361904361904Observability Estimate for the Fractional Order Parabolic Equations on Measurable SetsGuojie Zheng0M. Montaz Ali1College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, ChinaSchool of Computational and Applied Mathematics, University of the Witwatersrand (Wits), Johannesburg 2050, South AfricaWe establish an observability estimate for the fractional order parabolic equations evolved in a bounded domain Ω of ℝn. The observation region is F×ω, where ω and F are measurable subsets of Ω and (0,T), respectively, with positive measure. This inequality is equivalent to the null controllable property for a linear controlled fractional order parabolic equation. The building of this estimate is based on the Lebeau-Robbiano strategy and a delicate result in measure theory provided in Phung and Wang (2013).http://dx.doi.org/10.1155/2014/361904 |
| spellingShingle | Guojie Zheng M. Montaz Ali Observability Estimate for the Fractional Order Parabolic Equations on Measurable Sets Abstract and Applied Analysis |
| title | Observability Estimate for the Fractional Order Parabolic Equations on Measurable Sets |
| title_full | Observability Estimate for the Fractional Order Parabolic Equations on Measurable Sets |
| title_fullStr | Observability Estimate for the Fractional Order Parabolic Equations on Measurable Sets |
| title_full_unstemmed | Observability Estimate for the Fractional Order Parabolic Equations on Measurable Sets |
| title_short | Observability Estimate for the Fractional Order Parabolic Equations on Measurable Sets |
| title_sort | observability estimate for the fractional order parabolic equations on measurable sets |
| url | http://dx.doi.org/10.1155/2014/361904 |
| work_keys_str_mv | AT guojiezheng observabilityestimateforthefractionalorderparabolicequationsonmeasurablesets AT mmontazali observabilityestimateforthefractionalorderparabolicequationsonmeasurablesets |