Stability Of Wave Equations With Delay And Dynamic Boundary Conditions

Partial differential equations are a kind of very important equations in the field of mathematics.The wave equations studied in this paper belong to one of them,which mainly describe the vibration phenomenon of various waves in life.For example,sound wave,water wave and light wave,etc.Therefore,studying this kind of equations have great practical significance and application value.In this thesis,Faedo-Galerkin approximation,energy estimation,ordinary differential equation theory,and construction of Lyapunov functional methods are used to study the existence and stability of solutions for wave equations with delay and dynamic boundary conditions.In this thesis,we study the properties of the solutions for two kinds of wave equations with delay and dynamic boundary conditions.In Chapter 1,the background and significance of wave equations with delay and dynamic boundary conditions are introduced,as well as the research status.In Chapter 2,we mainly considers the wave equation with time delay,strong damping and dynamic boundary conditions.Faedo-Galerkin approximations and some priori estimates are used to prove the local existence and uniqueness of the solution,we prove the local existence and uniqueness of solution.The exponential stability of the system is obtained by using the energy perturbation method and the multiplier method.In chapter 3,we study the semilinear wave equations with time delay,viscoelastic damping and dynamic boundary conditions.By using energy perturbation method and multiplier method,we prove the polynomial stability of the energy under much weak conditions concerning memory effects.