Global attractor for a nonlinear wave equation arising in elastic waveguide model

The paper studies the longtime behavior of solutions to the initial boundary value problem (IBVP) for a nonlinear wave equation arising in an elastic waveguide model utt−Δu−Δutt+Δ2u−Δut−Δg(u)=f(x)utt−Δu−Δutt+Δ2u−Δut−Δg(u)=f(x). It proves that when the space dimension N≤5N≤5, under rather mild conditions the dynamical system associated with the above-mentioned IBVP possesses a global attractor which is connected and has finite fractal and Hausdorff dimension.