Asymptotic behavior to Bresse system with past history

Santos, Mauro; Soufyane, A.; Almeida Júnior, Dilberto

doi:10.1090/S0033-569X-2014-01382-4

Authors: Mauro de Lima Santos, A. Soufyane and Dilberto da Silva Almeida Júnior
Journal: Quart. Appl. Math. 73 (2015), 23-54
MSC (2010): Primary 74H40
DOI: https://doi.org/10.1090/S0033-569X-2014-01382-4
Published electronically: October 17, 2014
MathSciNet review: 3322725
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Abstract: In this paper we consider the Bresse system with past history acting in the shear angle displacement. We show the exponential decay of the solution if and only if the wave speeds are the same. On the contrary, we show that the Bresse system is polynomial stable with optimal decay rate. The systems of equations considered here introduce new mathematical difficulties in order to determine the asymptotic behavior. As far as the authors know, there have been no contributions made in this sense.

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