Global well-posedness and energy decay for a one dimensional porous-elastic
system subject to a neutral delay
Houssem Eddine Khochemane, Sara Labidi, Sami Loucif, Abdelhak Djebabla
Received July 10, 2023. Published online July 2, 2024.
Abstract: We consider a one-dimensional porous-elastic system with porous-viscosity and a distributed delay of neutral type. First, we prove the global existence and uniqueness of the solution by using the Faedo-Galerkin approximations along with some energy estimates. Then, based on the energy method with some appropriate assumptions on the kernel of neutral delay term, we construct a suitable Lyapunov functional and we prove that, despite of the destructive nature of delays in general, the damping mechanism considered provokes an exponential decay of the solution for the case of equal speed of wave propagation. In the case of lack of exponential stability, we show that the solution decays polynomially.
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Affiliations: Houssem Eddine Khochemane (corresponding author), École Normale Supérieure d'Enseignement Technologique de Skikda, Rue du 1er Novembre, 21000 Azzaba, Algeria, e-mail: khochmanehoussem@hotmail.com; Sara Labidi, University of Badji Mokhtar-Annaba, B. P. 12, 23000 Annaba, Algeria; Laboratory of Numerical Analysis, Optimization and Statistics (LANOS), 23000 Annaba, Algeria, e-mail: sarralabidi2222@gmail.com; Sami Loucif, Laboratory of Mathematics, Informatics and Systems (LAMIS), University of Larbi Tebessi, Route de Constantine, 12022 Tebessa, Algeria, e-mail: loucifsami2022@gmail.com; Abdelhak Djebabla, University of Badji Mokhtar-Annaba, B. P. 12, 23000 Annaba, Algeria; Laboratory of Mathematics, Dynamics and Modelization, 23000 Annaba, Algeria, e-mail: adjebabla@yahoo.com
