Longtime dynamics of the Kirchhoff equations with fractional damping and supercritical nonlinearity

The paper investigates the global well-posedness and the longtime dynamics of the Kirchhoff equations with fractional damping and supercritical nonlinearity: utt−M(‖∇u‖2)Δu+(−Δ)αut+f(u)=g(x)utt−M(‖∇u‖2)Δu+(−Δ)αut+f(u)=g(x), with α∈(12,1). The main results are focussed on the relationships among the growth exponent p   of the nonlinearity f(u)f(u), the global well-posedness and the longtime dynamics of the equations. We show that (i) even if p   is up to the supercritical range, that is, 1≤p