Global attractor for the Kirchhoff type equation with a strong dissipation

The paper studies the longtime behavior of the Kirchhoff type equation with a strong dissipation utt−M( u 2)Δu−Δut+h(ut)+g(u)=f(x). It proves that the related continuous semigroup S(t) possesses in the phase space with low regularity a global attractor which is connected. And an example is shown.