Preprint Article Version 1 This version is not peer-reviewed

# Regional Observability with Constraints on the State of Semilinear Parabolic Systems

Version 1 : Received: 1 December 2018 / Approved: 4 December 2018 / Online: 4 December 2018 (03:29:41 CET)

How to cite: Zouiten, H.; Boutoulout, A.; El Alaoui, F. Regional Observability with Constraints on the State of Semilinear Parabolic Systems. Preprints 2018, 2018120044 (doi: 10.20944/preprints201812.0044.v1). Zouiten, H.; Boutoulout, A.; El Alaoui, F. Regional Observability with Constraints on the State of Semilinear Parabolic Systems. Preprints 2018, 2018120044 (doi: 10.20944/preprints201812.0044.v1).

## Abstract

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.

## Subject Areas

semilinear systems; parabolic systems; enlarged observability; regional reconstruction; subdifferential method; HUM approach

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