Observability Estimate for the Fractional Order Parabolic Equations on Measurable Sets

Abstract EN

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).