Full paper in PDF:
$%J. Saint Jean Paulin and M. Vanninathan, Boundary sentinels in cylindrical domains, Rev. Mat. Complut. 14 (2001), no. 1, 271309.%$

Boundary Sentinels in Cylindrical Domains
Département de Mathématiques
Université de Metz
Ile du Saulcy
57045 Metz Cedex 01 — France
TIFR centre
P.O. Box 1234
Bangalore 560012 — India

Received: September 8, 1999
Revised: September 27, 2000


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.