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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 18
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Research Article

Attractors for partially damped systems of binary mixtures of solids

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Pages 5103-5122 | Received 22 Oct 2021, Accepted 12 Dec 2022, Published online: 29 Dec 2022
 

Abstract

This paper targets the long-time dynamics of a semilinear system modeling a binary mixture of solids with frictional dissipation mechanism acting only on the elastic equation and subjected to nonlinear source term. The coupling gives new contributions to the theory associated with nonlinear dynamics of partially damped semilinear systems of a binary mixture of solids. Using the quasi-stability methods, we prove the existence of a smooth finite-dimensional global attractor irrespective of the wave speeds of the system. Moreover, we establish the existence of exponential attractors.

2000 Mathematics Subject Classifications:

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

Additional information

Funding

M. M. Freitas thanks the CNPq for financial support [grant number 313081/2021-2]. T. A. Apalara extends his appreciation to the University of Hafr Al-Batin (UHB) for the continuous support. A. J. A. Ramos thanks the CNPq for financial support [grant number 310729/2019-0].

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