Longtime Dynamics of a Semilinear Lamé System

Bocanegra-Rodríguez L.E.; Silva M.A.J.; Ma T.F.; Seminario-Huertas P.N. · Journal of Dynamics and Differential Equations (2023) · DOI: 10.1007/s10884-021-09955-7

Resumen

This paper is concerned with longtime dynamics of semilinear Lamé systems ∂t2u-μΔu-(λ+μ)∇divu+α∂tu+f(u)=b, defined in bounded domains of R3 with Dirichlet boundary condition. Firstly, we establish the existence of finite dimensional global attractors subjected to a critical forcing f(u). Writing λ+ μ as a positive parameter ε , we discuss some physical aspects of the limit case ε→ 0 . Then, we show the upper-semicontinuity of attractors with respect to the parameter when ε→ 0 . To our best knowledge, the analysis of attractors for dynamics of Lamé systems has not been studied before.

Instituciones: Universidad Nacional del Callao