Global attractor for a class of Kirchhoff models

The paper studies the longtime behavior of solutions to the initial boundary value problem (IBVP) for a class of Kirchhoff models arising in elastoplastic flow utt−div{|∇u|m−1∇u}−Δut+Δ2u+h(ut)+g(u)=f(x). By combining the decomposition idea with the operate technique, it proves that under rather mild conditions, the dynamical system associated with above-mentioned IBVP possesses in different phase spaces a global attractor which is connected, respectively. For application, the fact shows that for the concerned elastoplastic flow the permanent regime (global attractor) can be observed when the excitation starts from any bounded set in phase space.