Stability conditions to Bresse systems with indefinite memory dissipation. Issue 6 (25th April 2020)

• Record Type: Journal Article
• Authors: Fatori, Luci Harue; de Oliveira Alves, Michele; Fernández Sare, Hugo D.
• Is Part Of: Applicable analysis. Volume 99:Issue 6(2020)
• Page Start: 1066
• Page End: 1084
• Publication Date: 2020-04-25
• Subjects: Scott Hansen; Bresse system -- indefinite dissipation -- strong stability -- exponential stability; 35B40 -- 47D06 -- 45D05; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1520982
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: We study the asymptotic behavior of Bresse system with non-dissipative kernel memory acting only in the equation of longitudinal displacement. We show that the exponential stability depends on conditions regarding the decay rate of the kernel and a new relationship between the coefficients of the system. Moreover, this new condition on the constants of the system is used to prove strong stability and exponential stability for the homogeneous case (frictional dissipation in the longitudinal equation).