Energy decay for a porous system with a fractional operator in the memory

Chahrazed Messikh; Soraya Labidi; Ahmed Bchatnia; Foued Mtiri; Chahrazed Messikh; Soraya Labidi; Ahmed Bchatnia; Foued Mtiri

doi:10.3934/era.2025096

Electronic Research Archive

2025, Volume 33, Issue 4: 2195-2215. doi: 10.3934/era.2025096

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Energy decay for a porous system with a fractional operator in the memory

1.
Department of Mathematics, Applied Mathematics Laboratory, Badji Mokhtar University, Annaba 23000, Algeria
2.
LR Analyse Non-Linéaire et Géométrie, LR21ES08, Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El Manar, Tunisia
3.
Department of Mathematics, Applied College in Mahayil, King Khalid University, Abha 61421, Saudi Arabia

Received: 30 December 2024 Revised: 07 April 2025 Accepted: 09 April 2025 Published: 15 April 2025

In this work, we examine a porous-elastic system with a fractional operator incorporated in the memory term, which acts exclusively on one equation within the system. Under appropriate conditions on the polynomially decreasing kernels of the memory type, we establish the result of polynomial decay.
- porous system,
- polynomial decay,
- memory term,
- relaxation function
Citation: Chahrazed Messikh, Soraya Labidi, Ahmed Bchatnia, Foued Mtiri. Energy decay for a porous system with a fractional operator in the memory[J]. Electronic Research Archive, 2025, 33(4): 2195-2215. doi: 10.3934/era.2025096

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Abstract

In this work, we examine a porous-elastic system with a fractional operator incorporated in the memory term, which acts exclusively on one equation within the system. Under appropriate conditions on the polynomially decreasing kernels of the memory type, we establish the result of polynomial decay.

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