Energy Decay Of Hyperbolic Coupling Systems With Memory Damping

Over the years,The problem of the initial value of hyperbolic equations with memory damping is widely cited in mathematical modeling of problems describing physics,biology,chemistry,and other fields.Many scholars have studied the well-posedness and stability of solutions to hyperbolic equations with memory damping.In this paper,the abstract hyperbolic equation coupling system with single memory damping and double memory damping are studied,and the multiplier method and energy perturbation method are used to prove the global existence and energy attenuation properties of the corresponding hyperbolic equation coupling system solution.This thesis is divided into three chapters.The first chapter mainly introduces the application background of nonlinear hyperbolic equations,gives the existence and stability of the initial value system of hyperbolic equations with memory damping and hyperbolic coupling equations,and gives some preliminary knowledge.In the second chapter,an abstract hyperbolic coupling system with a single memory damping is studied,the global existence of the abstract system solution is first given,and then the appropriate functional is constructed by multiplier method and energy perturbation method,and the stability result of the system energy is given,and the obtained result is applied to the specific volume hyperbolic equation coupling system.In the third chapter,a class of variable coefficient abstract hyperbolic coupling systems with double memory damping is studied,and the appropriate functional is constructed by using the multiplier method and the energy perturbation method,and the stability results of the system energy are given.In the fourth chapter,summarizes this thesis.