A model problem for boundary layers of thin elastic shells

We consider a model problem (with constant coefficients and simplified geom etry) for the boundary layer phenomena which appear in thin shell theory as the relative thickness epsilon of the shell tends to zero. For epsilon = 0 our problem is parabolic, then it is a model of developpable surfaces. Bou ndary layers along and across the characteristic have very different struct ure. It also appears internal layers associated with propagations of singul arities along the characteristics. The special structure of the limit probl em often implies solutions which exhibit distributional singularities along the characteristics. The corresponding layers for small epsilon have a ver y large intensity. Layers along the characteristics have a special structur e involving subspaces; the corresponding Lagrange multipliers are exhibited . Numerical experiments show the advantage of adaptive meshes in these prob lems. Mathematics Subject Classification. 73K15, 35B25.