Exact Controllability For Semilinear Wave Equations

The goal of this paper is to prove the exact controllability of equation in H01(Ω)×L2 (Ω), under the weak assumption: and with control h∈L2(Ω×(0,T)), a(x)∈C(Ω), a(x)= 0 in a, a(x)≥0 in the other space. This paper is divided into four chapters:In the first chapter, we mainly introduce some basic theory and method.In the second chapter, we mainly prove exact controllability of the system in some time, We use the Fixed Point Method in this chapter, so the chapter mainly describe the method.In the third chapter, we mainly study the observability estimates for the wave equation with bounded potential and prove Theorem 2, i. e.If T> 2max(l1,,1-l2), there exist two positive constants A1,B1> 0, such that for every c∈L∞(Ω×(0,T)) and every solution φ of (2.11) with initial date:In the fourth chapter, we prove the exact controllability in some space by boundary control.