Attractors for partially damped systems of binary mixtures of solids

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.

Keywords:

• Mixture of solids
• quasi-stability
• gradient systems
• global attractors

2000 Mathematics Subject Classifications:

• 35B40
• 35B41
• 37L30

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].