Carleman Estimates and Simultaneous Boundary Controllability of Uncoupled Wave Equations.

We consider two uncoupled wave equations with potentials on an interval; they both have the same Dirichlet boundary control at the left endpoint. First, we discuss the conservative case, and by transmutation, we obtain a simultaneous null controllability for the corresponding uncoupled heat equations. Afterward, in the nonconservative case, we prove global Carleman estimates for the adjoint system; the proof relies on the introduction of new variables, and the construction of appropriate weight functions. Finally, using the Hilbert uniqueness method of Lions, we solve the simultaneous boundary controllability problem. The paper ends with some final remarks and open problems. [ABSTRACT FROM AUTHOR]