Research On Dynamic Behavior Of A Class Of Nonlinear Evolution Equations With Time Delay Effect

Nonlinear evolution equation plays an important role in the field of mathematics.The appearance of dynamic boundary condition and time delay in the equation seriously affects the energy stability of the system and regularity of the solution.In this thesis,we mainly investigate a class of viscoelastic wave equations with dynamic boundary conditions and delay terms.More details are presented as follows:Firstly,we investigate the existence and stability of viscoelastic wave equations with dynamic boundary conditions and boundary time delay.By using Galerkin approximation,some prior estimates and some inequality techniques,we prove the local existence and uniqueness of the model under assumptions of the corresponding memory function and time delay effect.Also by using the perturbation energy method,we construct a suitable Lyapunov function to prove the exponential decay of energy.Secondly,we investigate the existence and stability of viscoelastic wave equations with dynamic boundary conditions and internal time delay.In the case of different relation between the coefficient of friction damping and the coefficient of delay term,by using Galerkin approximation,some prior estimates and some inequality techniques,we prove the local existence of the model.We obtain the exponential decay estimate of energy by constructing a suitable Lyapunov function.