Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Asymptotic behavior to Bresse system with past history


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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Mauro de Lima Santos
Affiliation: Faculdade de Matemática-Programa de Pós-Graduação em Matemática e Estatística Universidade Federal do Pará, Campus Universitario do Guamá, Rua Augusto Corrêa 01, Cep 66075-110, Pará, Brazil
Email: ls@ufpa.br

A. Soufyane
Affiliation: Faculty of Engineering and Applied Sciences, ALHOSN University, P.O. Box 38772, Abu Dhabi, United Arab Emirates
Email: asoufyane@hotmail.com

Dilberto da Silva Almeida Júnior
Affiliation: Faculdade de Matemática-Programa de Pós-Graduação em Matemática e Estatística Universidade Federal do Pará, Campus Universitario do Guamá, Rua Augusto Corrêa 01, Cep 66075-110, Pará, Brazil
Email: dilberto@ufpa.br

DOI: https://doi.org/10.1090/S0033-569X-2014-01382-4
Keywords: Bresse system, optimal result
Received by editor(s): December 14, 2012
Published electronically: October 17, 2014
Article copyright: © Copyright 2014 Brown University


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