Sensitivity problems for some shells with edges (Q1380891)

In this paper a kind of highly unstable linear problem, called ``sensitive problem'' [\textit{J. L. Lions} and \textit{E. Sanchez-Palencia}, C. R. Acad. Sci. Paris Sér. I 319, No. 9, 1021-1026 (1994; Zbl 0811.35027); \textit{J. L. Lions} and \textit{E. Sanchez-Palencia}, in: Prog. Nonlinear Differ. Equ. Appl. 22, 207-220 (1996; Zbl 0857.35033)], is considered. This sensitivity is connected with some cases of the limit behavior of shells. The latter may be of two different kinds, according to the geometric rigidity or lack of rigidity of the middle surface, submitted to the kinetic boundary conditions. The limit problem is concerned with membrane approximation in the case of geometrical rigidity as the corresponding system is of elliptic or hyperbolic type at elliptic or hyperbolic points of the surface. Then sensitivity is mainly concerned with elliptic problems with a part of the boundary free of kinematics boundary conditions as well as with certain surfaces with edges [\textit{M. Bernadou} and \textit{P. G. Ciarlet} Comput. Meth. appl. Sci. Eng., 2nd int. Symp., Versailles 1975, Lect. Notes Econ. math. Syst. 134, 89-136 (1976; Zbl 0356.73066)]. The elliptic case and some generalizations are considered.