Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 18, pp. 1-22.

Title: Null controllability of coupled systems of degenerate parabolic 
       integro-differential equations
       
Authors: Brahim Allal (Ibn Zohr Univ., Morocco)
         Genni Fragnelli (Tuscia Univ., Viterbo, Italy)
         Jawad Salhi (Moulay Ismail Univ. of Meknes, Morocco)
         
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.