We consider a model problem (with constant coefficients and simplified
geometry) for the boundary layer phenomena which appear in thin shell theory
as the relative thickness ε of the shell tends to
zero. For ε = 0 our problem is parabolic, then it is a
model of developpable surfaces. Boundary layers along and across the characteristic
have very different structure. It also appears internal layers associated
with propagations of singularities along the characteristics. The special
structure of the limit problem often implies solutions which exhibit
distributional singularities along the characteristics. The corresponding
layers for small ε have a very large intensity. Layers along
the characteristics have a special structure involving subspaces; the
corresponding Lagrange multipliers are exhibited. Numerical experiments
show the advantage of adaptive meshes in these problems.