Boundary controllability problems for the wave equation in a parallelepiped

AbstractThe wave equation in an N-dimensional parallelepiped with boundary control equal zero everywhere except of an edge of dimension N − 2 is considered. The other case which is investigated is the boundary control acting on a face of dimension N − 1 and depending on N − 1 independent variables (including t). It is proved that, in both cases, the system is not approximately controllable for any T > 0

Reconstructing the potential for the 1D Schrödinger equation from boundary measurements

International audienceWe consider the inverse problem of determining the potential in the dynamical Schrödinger equation on the interval by the measurement on the boundary. We use the Boundary Control method to recover the spectrum of the problem from the observation at either left or right end points. Using the specificity of the one-dimensional situation we recover the spectral function, reducing the problem to the classical one which could be treated by known methods. We apply the algorithm to the situation when only the finite number of eigenvalues are known and prove the convergence of the method