Stability Of Solution For Viscoelastic Wave Equation With Dynamic Boundary Conditions And Delay

The properties of solutions for the nonlinear partial differential equations have always been a hot research subject.The study of the well-posedness and stability of the solution for nonlinear partial differential equations is of great significance to both natural science and real life.In this paper,the local existence,stability and blow-up of solutions for viscoelastic wave equations are studied by using partial differential equation theory,the multiplier method,the Faedo-Galerkin method and the energy functional method.The thesis consists of three chapters.In Chapter 1,this chapter mainly introduces the research status of the wave equation with time delay and the research work of this paper.In Chapter 2,we consider the viscoelastic wave equation with Kelvin-Voigt damping,source term and delay,under dynamic boundary conditions.We study the relationship between the time delay and the friction damping.When the absolute value of the delay factor is less than friction damping coefficient and the absolute value of the delay factor is greater than or equal to friction damping coefficient,we prove the uniqueness of solutions,the stability of solutions and the blow-up of solutions by assuming different conditions.In Chapter 3,we consider the viscoelastic wave equation with Kelvin-Voigt damping,source term and time-varying delay,under dynamic boundary conditions.We prove the existence and uniqueness of solutions,the stability of solutions.