The Initial-Boundary Value Problem Of The Thermoelastic Coupled Beam Equations With Memory Team Under Axial Force

In this paper,we study the initial boundary value in the homogeneous boundary condition of the equations of thermoelastic coupled beam with memory term under the action of axial force.Using the Galerkin method,the paper has proved the existence and uniqueness of the weak solution,continuous dependence of the solution on the initial value,and the existence of regular solution.Besides,the existence of global solutions under the inhomogeneous variable boundary conditions has also been proved.The structure of this paper is as follows:In chapter 1,brief introduction of the background and development of the equations of thermoelastic coupled beam with memory term,and the main work of this paper.In chapter 2,basic knowledge used in this paper,including definitions,lemmas,and common inequalities.In chapter 3,using the Galerkin method to prove the existence and uniqueness of the weak solution for the equations of thermoelastic coupled beam with memory term,and continuous dependence of the solution on the initial value.In chapter 4,by appropriate reinforcement of the memory term and the source term assumptions,proving the existence of the regular solution after when the homogeneous boundary condition and the initial condition remain unchanged.In chapter 5,by appropriate reinforcement of the memory term and the source term assumptions,proving the existence of the global solution after when the homogeneous boundary condition and the initial condition remain unchanged.