The Glabal Solutions For The Nonlinear Viscosity-Elasticity Beam Equations Under Nonlinear Boundary Conditions

In this paper,we study one kind of nonlinear viscous-elastic supported beam subjected to axial forces and transverse load,considering both viscosity effect and nonlinear external daming,and obtain the existence and uniqueness theorem of global solutions for the equations under nonlinear boundary conditions by the Galerkin method.The first chapter mainly introduces the background and source of the research problem,as well as the main contents and research results of this paper.The second chapter mainly introduces some basic knowledge of this paper,including basic space and their relationship,and some lemma,concepts and basic assumptions.The third chapter mainly adopts the Galerkin method,studies the initial boundary value problem of the dissipative viscoelastic beam equation under the nonlinear boundary condition,then obtains theexistence and uniqueness of the whole solution of the equation.In the fourth chapter,the initial boundary value problem of beam equations under nonlinear boundary conditions with viscosity is studied based on the Galekin method,and the whole solution of the equation is verified.In the fifth chapter,the research results of this paper are prospected.