Observability Estimate for the Fractional Order Parabolic Equations on Measurable Sets

摘要

We establish an observability estimate for the fractional order parabolic equations evolved in a bounded domainΩofℝn. The observation region isF×ω, whereωandFare measurable subsets ofΩand (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).