Energy Decay Estimates For Weakly Coupled String-riser System

In this thesis,the long-term characteristics of a series of weakly coupled string-riser systems are studied.The semigroup method and multiplier technique are used to prove the existence and uniqueness of the solution and energy decay estimation of systems,and the different cases are compared.This thesis is divided into three chapters.In chapter 1,we mainly introduce the physical background of string-riser weakly coupled system,as well as the specific application and results of related coupling system,and give the preparatory knowledge of abstract setup.In Chapter 2,the string-riser weakly coupled system with local friction damping is studied.The semigroup method is used to prove the existence and uniqueness of the solution,and the multiplier technique is combined to obtain that the two coupling systems are not exponentially stable,and the exact polynomial decay rate of their energy functional is given.In Chapter 3,the string-riser weakly coupled system with thermoelasticity is studied.The semigroup method and multiplicator technique are also used to prove the existence and uniqueness of the solution that the system is not exponentially stable,and the exact polynomial decay rate is obtained.In Chapter 4,we summarize the thesis.