The Stabilization Of Pseudo Control Parabolic System

In this paper,we mainly study the stability of pseudo parabolic partial differential equation in the fllowing form:? = [0,1].First of all,we want to prove the existence and uniqueness of the solution.After some converts,we use the method of Separation of variables obtain the solution of the system,and we have prove the uniqueness of this solution.By the change of f(t),the system have two cases: Open loop system and Closed loop system.When the system is a Closed loop system and initial with boundary to meet certain conditions,we proved that the solution is global exponentially stable in H~1-norm.When the system is a Open loop system,it is also a Pseudo Parabolic Control System with boundary feedback.We use Lyapunov function method obtain the specific forms of boundary feedback.We prove the system solution with this feedback law is global exponentially stable in H~1-norm.