Long-Time Dynamic Behavior Of Kirchhoff-Type Plate Equations With Nonlocal Weak Damping And Anti-Damping

In this thesis,we mainly study the global well-posedness,dissipative property,the existence of global attractors of the Kirchhoff-type plate equations with nonlocal weak damping and anti-damping.The details are as follows:First,when the nonlinear term g satisfies subcritical growth,we prove the global well-posedness of the linear Kirchhoff-type plate equation with nonlocal weak damping and anti-damping by using the theory concerning the well-posedness for the evolution equation containing an m-accretive operator with local Lipschitz perturbation.We demonstrate the dissipative property of the system by constructing a new Gronwall inequality.Then,we prove the asymptotic compactness of the system by using(C)conditions,and finally obtain the existence of global attractors.Next,Combined with the monotone of the nonlocal weak damping term k‖u_t‖~pu_t,we use the monotone operator theory to establish the global well-posedness of the nonlinear Kirchhoff-type plate equation with nonlocal weak damping and antidamping.Secondly,we prove the dissipative property of the system by constructing a new Gronwall inequality.Then we obtain the asymptotic smoothness of the system by using a prior estimation and energy reconstruction methods,and then we prove the existence of global attractors of the system.