Exact Controllability And Feedback Stabilization Of Coupled Degenerate Wave Equations

Partial differential equation is a very important branch of mathematics,and degenerate wave equation is an important part of partial differential equation.With the development of science and technology,it is found that partial differential equations are more and more closely related to other disciplines,especially in physics,biology,finance and other disciplines.Most literatures have studied the boundary controllability,blow-up of solutions and energy decay of partial differential equations.However,there is little research on the degenerate wave equation.Therefore,the boundary exact controllability and feedback stabilization of coupled degenerate wave equation are analyzed qualitatively in this paper.In the first chapter,firstly,the current situation of the wave equation,the degenerate wave equation and the related problems of the coupled wave equation with different boundary is given.In the second chapter,we discuss the exact controllability of the coupled degenerate wave equation,and apply the multiplier method to establish the corresponding.observability inequality,and finally,according to the Hilbert uniqueness method(HUM),it is proved the boundary exact controllability of the coupled degenerate wave equation.In the third chapter,the feedback stabilization of coupled degenerate wave equation with boundary damping is studied.Firstly,the large dissipation operator is constructed to prove the existence of the solution of the system.Then the energy functional of the system is defined,the multiplier method is used to deal with the items in the energy function.Finally,the decay of the system solution is proved.