The Global Solution For A Class Coupled Of Nonlinear Abstract Rod And Beam Equations

In this paper, we studied the existence of the global weak solution for an abstrac-t coupled of nonlinear rod equations by using Faedo-Galerkin method, that is the following rod equations under the initial conditions and studied the existence of the global weak solution for the following beam equations by using the same method under the initial conditions Then we improve the smoothness of the initial data u0, u1, u0, u1and f, g by limiting the range of a and β of the (3), and get a more smoothly solution, where Ω= (0,l), l> 0,0<β≤α≤1, t ∈[0,T](0< T< ∞), functions M and N satisfy certain conditions, A is a positive self-adjoint operator defined in H.