an:01437488
Zbl 1004.74050
Karamian, Philippe; Sanchez-Hubert, Jacqueline; Sanchez Palencia, ??varisite
A model problem for boundary layers of thin elastic shells
EN
M2AN, Math. Model. Numer. Anal. 34, No. 1, 1-30 (2000).
00062871
2000
j
74K25 74G10 35Q72
thin shell theory; boundary layer; developable surfaces; propagation of singularities; characteristics; Lagrange multipliers
Authors' abstract: We consider a model problem (with constant coefficients and simplified geometry) for boundary layer phenomena which appear in thin shell theory as the relative thickness \(\varepsilon\) of the shell tends to zero. For \(\varepsilon = 0\) our problem is parabolic, for \(\varepsilon>0\) the equations can be considered as a model of developable surfaces. Boundary layers along and across the characteristics have very different structures. There also appear internal layers associated with the propagation of singularities along the characteristics. The 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.
Old??ich John (Praha)