Full paper in PDF:
$%J. Saint Jean Paulin and M. Vanninathan, Boundary sentinels in cylindrical domains, Rev. Mat. Complut. 14 (2001), no. 1, 271–309.%$

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 (1992) 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 non-zero boundary data of mixed type and an exact controllability problem. Further, we characterize the so called “stealthy pollution terms” present in the model.

2000 Mathematics Subject Classification: 93B05, 93C20, 93C95, 35L20, 35L05.