Stability of attractors for the Kirchhoff wave equation with strong damping and critical nonlinearities

The paper investigates longtime dynamics of the Kirchhoff wave equation with strong damping and critical nonlinearities: utt−(1+ϵ‖∇u‖2)Δu−Δut+h(ut)+g(u)=f(x), with ϵ∈[0,1]. The well-posedness and the existence of global and exponential attractors are established, and the stability of the attractors on the perturbation parameter ϵ is proved for the IBVP of the equation provided that both nonlinearities h(s) and g(s) are of critical growth.