Pullback dynamics of a non-autonomous mixture problem in one dimensional solids with nonlinear damping

Mirelson M. Freitas; Alberto L. C. Costa; Geraldo M. Araújo

doi:10.3934/cpaa.2020037

Article Contents

2020, Volume 19, Issue 2: 785-809. Doi: 10.3934/cpaa.2020037

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Pullback dynamics of a non-autonomous mixture problem in one dimensional solids with nonlinear damping

1.
Federal University of Pará, Raimundo Santana Street s/n, Salinópolis PA, 68721-000, Brazil
2.
Institute of Exact and Natural Sciences, Doctoral Program in Mathematics, Federal University of Pará, Augusto corrêa Street, Number 01, 66075-110, Belém PA, Brazil

Received: October 31, 2018

Revised: February 28, 2019

Published: October 2019

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Abstract

This paper is devoted to study the asymptotic behavior of a non-autonomous mixture problem in one dimensional solids with nonlinear damping. We prove the existence of minimal pullback attractors with respect to a universe of tempered sets defined by the sources terms. Moreover, we prove the upper-semicontinuity of pullback attractors with respect to non-autonomous perturbations.

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Mathematics Subject Classification: Primary: 35B40, 35L53, 35B41; Secondary: 37B55.

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References

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