New cases of propagation of singularities along characteristic boundaries for model problems of shell theory

We continue a previous work [1] on propagation of singularities for model problems of thin shell theory in the parabolic and hyperbolic cases. The singularities along the characteristic boundaries are considered using extensions of the solutions out of the domain, adapted to either free or fixed boundaries. The corresponding transport equations are given except for the case of a characteristic fixed boundary for a hyperbolic shell, where the phenomenon is non local, but depends on the whole domain.