Stability conditions to Bresse systems with indefinite memory dissipation

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).

COMMUNICATED BY:

• Scott Hansen

KEYWORDS:

• Bresse system
• indefinite dissipation
• strong stability
• exponential stability

2010:

• 35B40
• 47D06
• 45D05

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

L. H. Fatori is supported by Fundação Araucária/SETI, grant # 308/2012.