A Study On The Solution For A Class Of Plate Equations With Nonlocal Damping Term

In this paper,we study the existence,asymptotic behavior and blow-up of solutions for a class of initial boundary value problems of plate equations with nonlinear nonlocal damping terms and source terms as follows:(?)where ?(?)Rn is a bounded domain with smooth boundary(?)and M(||?u||22 is the coefficient of the nonlocal damping term.By using the classical Faedo-Galerkin method,the existence of local solutions is proved in two cases of nonlinear nonlocal damping terms which are degenerate and non-degenerate respectively.Furthermore,the potential well theory and the continuous continuation theorem are used to prove the existence of the global solutions when the initial value is located in the potential well.For the non-degenerate case,Nakao's inequality is used to obtain the decay estimation of the global solutions under the conditions that the initial value is located in the potential well and the initial energy meets certain conditions.For the degenerate case,by constructing a differential inequality,the sufficient condition of blow-up of the solution at finite time is obtained when p>m and the initial conditions are out of the potential well set.