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On sensitive elliptic singular perturbation problems and logarithmic oscillations: the case of shells with edges
Author(s) -
Merabet I.,
SanchezPalencia E.
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2607
Subject(s) - singular perturbation , mathematics , logarithm , mathematical analysis , perturbation (astronomy) , instability , compressibility , elasticity (physics) , boundary value problem , singular solution , physics , mechanics , quantum mechanics , thermodynamics
This work deals with singular perturbation problems depending on small positive parameter ϵ . The limit problem as ϵ → 0 has no solution within the classical theory of PDEs, which uses distribution theory. A very particular and less‐known phenomenon appears: large oscillations. These problems exhibit some kind of instability; very small and smooth variations of the data imply large singular perturbations of the solution. That kind of problems appears in elasticity for highly compressible two‐dimensional bodies and thin shells with elliptic middle surface with a part of the boundary free. Here, we consider certain properties of that oscillations and extend the theory to shells with edges. Copyright © 2012 John Wiley & Sons, Ltd.