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Sensitivity problems for some shells with edges. (English) Zbl 0935.35041
In this paper a kind of highly unstable linear problem, called “sensitive problem” [J. L. Lions and E. Sanchez-Palencia, C. R. Acad. Sci. Paris Sér. I 319, No. 9, 1021-1026 (1994; Zbl 0811.35027); J. L. Lions and 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 [M. Bernadou and 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.

MSC:
35J40 Boundary value problems for higher-order elliptic equations
74K25 Shells
35B35 Stability in context of PDEs
35B25 Singular perturbations in context of PDEs
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