On internal and boundary layers with unbounded energy in thin shell theory. Hyperbolic characteristic and non-characteristic cases

Abstract

We consider the system of equations of Koiter shell theory in a slightly simplified form, in the case when the limit (for small thickness) problem is hyperbolic, i.e., the principal curvatures of the middle surface are everywhere of opposite signs. Under loadings not belonging to the dual of the energy space of the limit problem, the energy of the solutions grows without limit as the thickness tends to zero and concentrates on internal or boundary layers. Two cases are considered, when the singular loadings are applied either along a non-characteristic or a characteristic curve. In both cases we define and prove the convergence to the leading order in the layers.