Exponential decay and well-posedness for a one-dimensional porous-elastic system with distributed delay. Issue 14 (26th October 2021)

• Record Type: Journal Article
• Authors: Khochemane, Houssem Eddine; Bouzettouta, Lamine; Guerouah, Amin
• Is Part Of: Applicable analysis. Volume 100:Issue 14(2021)
• Page Start: 2950
• Page End: 2964
• Publication Date: 2021-10-26
• Subjects: M. Fang; Porous-elastic system -- semigroup theory -- distributed delay -- exponential stability -- Lyapunov method; 35L70 -- 35B40 -- 93D20; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1703958
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we consider a one-dimensional porous-elastic system with distributed delay term acting on the porous equation. Under suitable assumptions on the weight of distributed delay, we establish the well-posedness of the system by using semigroup theory and we show that the dissipation given by this complementary control stabilizes exponentially the system for the case of equal speeds of wave propagation.