Long-time dynamics of the strongly damped semilinear plate equation in RN

We investigate the initial-value problem for the semilinear plate equation containing localized strong damping, localized weak damping and nonlocal nonlinearity. We prove that if nonnegative damping coefficients are strictly positive almost everywhere in the exterior of some ball and the sum of these coefficients is positive a.e. in Rn, then the semigroup generated by the considered problem possesses a global attractor in H2(Rn)×L2(Rn). We also establish the boundedness of this attractor in H3(Rn)×H2(Rn).