Research On Initial And Boundary Problems For Coupling Beam Equations With Nonlinear Damping

In this paper, the existence of global weak solution for a class of Kirchhoff coupling beam equations with nonlinear damping under the initial condition and the boundary condition is proved by using the Galerkin method, the existence and uniqueness of global strong solution for it are proved by using the fixed point theory, and the existence of attractor for it is also proved.All spaces used by this study are Hilbert space.The structure of this paper is as follows:In the first chapter, the development and research status of Kirchhoff nonlinear par-tial differential equation(s) related to this paper are summarized and described briefly.In the second chapter, some Lemmas, concepts and assumptions are introduced, and all mathematical symbols used by this paper are explained.In the third chapter, by using the Faedo-Galerkin method, the existence of global weak solution for the system is proved,by using the fixed point theory, the existence and uniqueness of global strong solution for the system are proved.In the fourth chapter, according to the semi-group theory, the existence of global attractor for the system is proved.In the fifth chapter,the main work of this paper is summarized and the next re-search program is discussed.