Exact Controllability Of The Nonlinear Wave Equations With Variable Coefficient

This paper mainly discusses the nonlinear problem:if f satisfying the condition of , the exact controllability of the system (1.1) holds in H01(Ω)×L2(Ω) with the function g ∈L2(V×[0, T]) perform a control functions in V set, which is the open and non empty subset of Ω.The paper includes five chapters.The first chapter is the introduction, the chapter introduces the definition of exact controllability of the system (1.1) and explains some signs of the paper.The second chapter is concerned with the energy estimates of the non homogeneous equationThe third chapter is concerned with the energy estimates of the homogeneous equationIn the fourth chapter,we use the energy estimates of the first and the second chapter to prove the observability estimates of the (3.1) system,On the basis of the earlier chapters, the fifth chapter prove the exact controllability of the (1.1) system with Hilbert Unique Method.