Brahim Allal, Genni Fragnelli, Jawad Salhi
Abstract:
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 |
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Genni Fragnelli Department of Ecological and Biological Sciences Tuscia University Largo dell'Università 01100 Viterbo, Italy email: genni.fragnelli@unitus.it |
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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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