Lamé system with weak damping and nonlinear time-varying delay

This article is concerned with the stability and dynamics for the weak damped Lamé system with nonlinear time-varying delay in a bounded domain. Under some appropriate assumptions, the global well-posedness and asymptotic stability are shown in the case where the delay coefficient is upper dominated by the damping one. Moreover, the finite dimensional global and exponential attractors have also been presented by relying on quasi-stability arguments. The results in this article is an extension of Ma, Mesquita, and Seminario-Huertas’s recent work [ Smooth dynamics of weakly damped Lamé systems with delay , SIAM J. Math. Anal. 53 (2021), no. 4, 3759–3771].