Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain
The exact boundary controllability of linear and nonlinear Korteweg-de Vries equation on bounded domains with various boundary conditions is studied. When boundary conditions bear on spatial derivatives up to order 2, the exact controllability result by Russell-Zhang is directly proved by means of Hilbert Uniqueness Method. When only the first spatial derivative at the right endpoint is assumed to be controlled, a quite different analysis shows that exact controllability holds too. From...