Asymptotic Behavior Of Solutions Of Wave Equations With Wentzell Boundary Memory Damping

In this paper,we study the energy decay of solutions of linear wave equations with Wentzell boundary and memory damping on the boundary and the characteristics of convergence rate of solutions in the process of energy decay.Compared with the work done by predecessors,the strong stability and weak convergence rate of the equilibrium solution of the equation are solved by using weaker memory boundary damping.The study of the equation is placed in two different regional conditions,from the bounded region of two-dimensional unit square to the bounded region of R~n-dimension.In both of the regional conditions,abstract development equations are constructed by deforming the original equation.In the two-dimensional unit square region,the proof method is to establish bilinear continuous function and use Fredholm selection theory.The strongly continuous semigroup theory of linear operators is used in dimensional bounded regions.It is proved that the equilibrium solution of the wave equation has strong stability under two conditions,and the energy of any non-zero solution decreases monotonically with time and converges to 0.The attenuation characteristic of the energy solution of the wave equation is studied by reconstructing the original equation into an abstract Cauchy problem,obtaining that the spectrum of the corresponding operator matrix has no pure imaginary value,and then analyzing the eigenvalue family of the operator matrix,proving that the energy solution of the wave equation has slow decay rate.