Boundary sentinels in cylindrical domains

Abstract

We study a model describing vibrations of a cylindrical domain with thickness e > 0. A characteristic of this model is that it contains “pollution terms” in the boundary data and “missing terms” in the initial data. The “method of sentinels” of J.L. Lions [7] is followed to construct a sentinel using the observed vibrations on the boundary. Such a sentinel, by construction, provides information on pollution terms independent of missing terms. This requires resolution of initial-boundary value problems with nonzero boundary data of mixed type and an exact controllability problem. Further, we characterize so called “stealthy pollution terms” present in the model.