Porous elastic system with Kelvin–Voigt: analyticity and optimal decay rate. Issue 8 (24th May 2022)

• Record Type: Journal Article
• Authors: Oliveira, M. L. S.; Maciel, E. S.; Dos Santos, M. J.
• Is Part Of: Applicable analysis. Volume 101:Issue 8(2022)
• Page Start: 2860
• Page End: 2877
• Publication Date: 2022-05-24
• Subjects: M. Fang; Porous-elasticity -- lack of stability -- analytic semigroup -- polynomial decay -- optimality; 35B35 Stability -- 35B40 Asymptotic behavior ofsolutions; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1828368
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this work we analyze the porous elastic system with a viscoelastic dissipative mechanism of Kelvin–Voigt type. We prove that the semigroup associated with the model is analytic if and only if the viscoelastic damping is present in both equations of the system. Otherwise, there exist lack of exponential stability, independently of any relationship between the coefficients. This result is different to all others related to porous-elastic model with partial dissipation. In this case we prove that the semigroup decays as t − 1 / 2 . Moreover we show that the rate is optimal.