Observability Estimate for the Fractional Order Parabolic Equations on Measurable Sets. (27th March 2014)

• Record Type: Journal Article
• Authors: Zheng, Guojie; Ali, M. Montaz
• Other Names: Li Sheng-Jie Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-03-27
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/361904
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We establish an observability estimate for the fractional order parabolic equations evolved in a bounded domain Ω of ℝ n . 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).