On the Exact Boundary Controllability of Semilinear Wave Equations

We address the exact boundary controllability of the semilinear wave equation ytt -∆y + f (y) = 0 posed over a bounded domain Ω of R d .Assuming that f is continuous and satisfies the conditionβ for some β small enough and some p ∈ [0, 3/2), we apply the Schauder fixed point theorem to prove the uniform controllability for initial data in L 2 (Ω) × H -1 (Ω).Then, assuming that f is in C 1 (R) and satisfies the condition lim sup |r|→∞ |f (r)|/ ln p |r| β, we apply the Banach fixed point theorem and exhibit a strongly convergent sequence to a state-control pair for the semilinear equation.