Observability estimate for the fractional order parabolic equations on measurable sets
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)].
scientific article; zbMATH DE number 7022225