ASYMPTOTIC BEHAVIOR FOR THE KIRCHHOFF TYPE PLATE EQUATION WITH NONLOCAL NONLINEAR DAMPING

The current paper is devoted to the existence and regularity of a global attractor for a Kirchoff type plate equation with nonlocal nonlinear damping u(tt)+Delta(2)u+delta(||del u||(2))psi(u(t))+(rho-alpha integral(Omega) |del u|(2)dx)Delta u+ phi(u) = h(x). We establish that when the growth exponent p of the nonlinearity phi(u) satisfies 2 <= p <= p*, the problem is well-posed and the related solution semigroup still has a global attractor in the natural energy space H = H-2(Omega) boolean AND H-0(1)(Omega) x L-2(Omega), where p* = 10q/q+1 (>= 5) is a new exponent depending on q is an element of [1, 9) which is the growth index of the nonlinear damping term psi(u(t)). Finally, by decomposing the weak solutions into two parts and conducting elaborate calculations, we derive the regularity of the global attractors.