Attractors And Their Stability For The Extensible Beam Equations With Nonlocal Damping

In this paper,we are concerned with the well-posedness,the existence and stability of attractors of the following extensible beam equations with nonlocal nonlinear damping:(?)where ? ?[1,2),?(?)RN is a bounded domain with the smooth boundary (?)?,h(x)is an external force term,f(u)is a nonlinear source term.We are concerned with the wellposedness of weak solutions in H=V2×L2 when the dissipative index a and the growth exponent of the nonlinearity f(u)satisfy the following conditions:1?p<p*=(N+4)/((N-4)+)1?p?p*=(N+4)/((N-4)+).When t>0,the solutions have higher global regularity.And we prove that the weak solution is the strong one.Moreover,we prove the existence of global attractors and exponential attractors of the corresponding operator semigroups in the energy phase space H.Besides,we prove the existence of strong global attractors and exponential attractors.And we get the upper semicontinuity of strong global attractors on the dissipative index a.