Solutions Of Thermoelastic Coupled Beam Equations With Memory Terms

The paper is devoted to the research of thermoelastic coupled beam equations with memory terms.Two memory terms both in the heat conduct equation and in the beam equation are considered.Existence,uniqueness and continuous dependence upon initial data of the weak solution are proved by the Galerkin method.Futhermore,existence of the strong solution and classical solution are proved. The paper is arranged as follows:In Chapter l,the development and present situation of the thermoelastic coupled equations with memory terms and the main work of this paper are briefly introduced.In Chapter 2,essential knowledge used in this paper including basic spaces,lemmas and assumptions are given.In Chapter 3,existence,uniqueness and continuous dependence upon initial data of the weak solution of thermoelastic coupled beam equations with memory terms are proved by the Galerkin method.In Chapter 4,with the condition of initial data and boundary unchanged,existence of the strong solution are proved under the proper assumptions of memory terms and source terms.In Chapter 5,existence of the classical solution are proved under the strengthened condition of memory terms and source terms furtherly.