A Class Of Time Discrete Wave Equations:Boundary Observability And Control

In this paper,we study the exact boundary and observability of the wave equation with some of the variables are discreted.It mainly studies the following two kinds of cir-cumstances. The first case is the equation with λ≤λ*, λ*=(N-2)/4and the time discretization.Then we study the equation Wether the total energy of solutions can be estimated uniformly in terms of the energy concentrated on the boundary as the net-spacing hâ†'0.In this article the introduction describes the problem where it came from, equation of time discretization, two or three chapter of well-posedness, observability and control-lability, in the fifth chapter, study on the one-dimensional case observability.