Initial-boundary Value Problems For Thermoelastics Coupled Beam Equations With Memory Terms

In recent years,the initial-boundary value problem of thermoelastic coupled beam e-quations has always been a hot topic.This is because in some practical applications,the deformation law of the beam itself is not only necessary,but also the effects of tempera-ture changing.In this paper,a class of thermoelastic coupled beam equations with memory terms is presented,and the problem of the well-posedness beam equations under homoge-neous boundary conditions is discussed in this paper,combining the two factors of the beam and temperature above.In the process of proving,we use the Galerkin method to prove the existence of weak solutions,and use some techniques such as Young inequality and Schwarz inequality.Finally,the existence of strong solutions to the problem is further studied when the smoothness of the initial value is further strengthened.The full text is divided into five chapters.The first chapter describes the background and research status of the thermoelastic cou-pled beam equations,and elaborates the main work of this paper.The second chapter gives some basic knowledge to facilitate the proof of this paper.The third chapter,the existence,uniqueness and continuous dependence of the weak solutions of the thermalelastic coupling beam equations with memory terms are proved by using the Galerkin method and the inequality technique.The fourth chapter,the smoothness of initial values is further improved,and the exis-tence of strong solutions is proved.The fifth chapter is a summary and prospect of this article.