Long-time dynamics of ternary mixtures with localized dissipation

Abstract

In this paper, we are considering a system modeling a mixture of three interacting continua with localized nonlinear damping acting in an arbitrary small region of the interval under consideration and external forces. The main goal is to construct a smooth global attractor with a finite fractal dimension using the recent quasi-stability theory. We also study the convergence of these attractors with respect to a parameter ϵ that multiplies the external forces. This study generalizes and improves the previous paper by Freitas et al. [Discrete Contin. Dyn. Syst. B 27, 3563 (2021)].