Rapid Exact Controllability Of The Semilinear Hyperbolic Equations

This work is addressed to a study of the (global) rapid exact controllability of aclass of semilinear hyperbolic equation with a locally moving distributed controllers,where the nonlinearity f(s) is assumed to satisfy the growth condition: (?)(f(s)/(s ln~h|s|))=0, (?)h∈[0, 2).As a key preliminary to prove this controllability result, we establish an explicit ob-servability estimate for the linear hyperbolic equation.