Regional Observability with Constraints on the State of Semilinear Parabolic Systems

The paper is devoted to the investigation of regional observability with constraints on the state of semilinear parabolic systems. The purpose is to reconstruct the initial state between two prescribed functions only on an internal subregion $\omega$ of the system evolution domain $\Omega$. The proofs use two approaches, the subdifferential and HUM approach. Finally, a numerical example is provided to verify the effectiveness of our theory results.