On porous-elastic systems with Fourier law. Issue 6 (26th April 2019)

• Record Type: Journal Article
• Authors: Santos, M. L.; Campelo, A. D. S.; Oliveira, M. L. S.
• Is Part Of: Applicable analysis. Volume 98:Issue 6(2019)
• Page Start: 1181
• Page End: 1197
• Publication Date: 2019-04-26
• Subjects: Porous-elasticity -- exponential decay -- polynomial decay; 35Q70 -- 35B40 -- Secondary: 74F05; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1419197
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this work, we study the asymptotic behavior of a porous elastic system coupled with the Fourier law. We show that the norm of resolvent operator is limited uniformly along the imaginary axis and we deduce that if the wave propagation speed are equal, then the system achieves exponential stability. On the other hand, if wave propagation speeds are different, then we show that the resolvent operator is not limited uniformly along the imaginary axis. This leads us to conclude that in general the model is polynomially stable.