Observability estimate for the fractional order parabolic equations on measurable sets
type: Item
instance of: scholarly article
title: Observability estimate for the fractional order parabolic equations on measurable sets
zbMATH Open document ID: 1406.93068
DOI: 10.1155/2014/361904
author: Guojie Zheng
author: M. Montaz Ali
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We establish an observability estimate for the fractional order parabolic equations evolved in a bounded domain \(\Omega\) of \(\mathbb{R}^n\). The observation region is \(F \times \omega\), where \(\omega\) and \(F\) are measurable subsets of \(\Omega\) 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 [\textit{K. D. Phung} and \textit{G. Wang}, J. Eur. Math. Soc. (JEMS) 15, No. 2, 681--703 (2013; Zbl 1258.93037)].
Mathematics Subject Classification ID: 93B07
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 93C20
zbMATH DE Number: 7022225
zbMATH Keywords: observability estimate
zbMATH Keywords: fractional order parabolic equations
Wikidata QID: Q57931926
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/361904
OpenAlex ID: W2081286198
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description: scientific article; zbMATH DE number 7022225