| In this paper we study the existence and the asymptotic behavior of global weak solution of the following initial boundary value problems for an beam equation with structural damping:where are constants, are positive integers.In Chapter 2,by constructing the modified potential well W associated with (1)-(3) and using a new Gronwall type integral inequality,we obtain the global weak solution for the problem (1)-(3) with r>0,by applying Galerkin method. The main resut is the following:Theorem 1 Suppose that andthen the problem (1)-(3) has global weak solution.In Chapter 3, we get the asymptotic behavior of the global weak solution of the problem(1)-(3) with r>0 by using Nakao difference inequality. The main reslut reads as:Theorem 2 Suppose that the problem (1) - ( 3 ) has global weak solution, andwhere [t-1] + = max{t-1,0} ,and k, (E(0)) are positive constant depending on || uox|| and || MI || .In Chapter 4 , we prove the existence and uniqueness of the global weak solution for the problem (1)-(3) with r<0 by Galerkin method. The main result is the following:Theorem 3 Suppose that r<0, , then the problem (1)-(3) has the unique global weak solution. |
