Electron. J. Differential Equations, Vol. 2023 (2023), No. 18, pp. 1-22.

Null controllability of coupled systems of degenerate parabolic integro-differential equations

Brahim Allal, Genni Fragnelli, Jawad Salhi

This article concerns the null controllability of a coupled system of two degenerate parabolic integro-differential equations with one locally distributed control force. Since the memory terms do not allow applying the standards Carleman estimates directly, we start by proving a null controllability result for an associated nonhomogeneous degenerate coupled system employing new Carleman estimates with appropriate weight functions. As a consequence, we deduce the null controllability result for the initial memory system by using the Kakutani's fixed point Theorem.

Submitted October 9, 2021. Published February 22, 2023.
Math Subject Classifications: 35K65, 45K05, 93C05, 93B05.
Key Words: Carleman estimates; parabolic systems involving memory terms; observability inequality; null controllability.
DOI: https://doi.org/10.58997/ejde.2023.18

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Brahim Allal
Ibn Zohr University
Faculty of Applied Sciences
IMIS Laboratory
86153 At-Melloul, Morocco
email: b.allal@uiz.ac.ma
Genni Fragnelli
Department of Ecological and Biological Sciences
Tuscia University
Largo dell'Università
01100 Viterbo, Italy
email: genni.fragnelli@unitus.it
Jawad Salhi
Moulay Ismail University of Meknes
FST Errachidia
MAIS Laboratory, MAMCS Group
P.O. Box 509 Boutalamine
52000 Errachidia, Morocco
email: j.salhi@umi.ac.ma

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